Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
At an annual rate of 10% compounded continuously, the number of years in which a principal
triples is
1)
A)
ln 3
0.10 .
B)
ln 0.10
3.
C)
3
ln 0.10 .
D)
e0.30.
E)
0.10
ln 3 .
2)
A $10,000 loan is amortized by equal semiannual payments over 5 years. If the interest rate is 8%
compounded semiannually, then the principal repaid in the first payment is
2)
A)
$795.38.
B)
$762.47.
C)
$832.91.
D)
$853.64.
E)
$806.21.
3)
Suppose a person invests $20,000 in a business venture that guarantees the same cash flow at the
end of every quarter for four years. If the investment earns interest at the rate of 16% compounded
quarterly, then each cash flow is
3)
A)
$1716.40.
B)
$916.40.
C)
$2341.23.
D)
$1527.52.
E)
$1917.39.
4)
A trust fund is to be established by a single payment so that at the end of 15 years, there will be
$20,000 in the fund. If the fund earns interest at the rate of 8% compounded semiannually, how
much should be deposited initially into the fund?
4)
A)
$7014.27
B)
$6166.38
C)
$7143.56
D)
$11,105.30
E)
$6472.42
5)
If money earns interest at an annual rate of 8% compounded continuously, then the value (in
dollars) of $10,000 due at the end of five years is
5)
A)
10,000e0.4
B)
10,000(1.08)–5
C)
10,000e–0.4
D)
10,000(1.08)5
E)
e0.4
10,000
6)
If an investment of $12,000 earns interest at an annual rate of 7% compounded continuously, then
the value (in dollars) of the investment ten years from now is
6)
A)
12,000– 0.7
B)
12,000e0.7
C)
e0.7
12,000
D)
12,000(1.07)–10
E)
12,000(1.07)10
7)
A debt of $2000 due in one year is to be repaid by a payment due two years from now and a final
payment of $1000 three years from now. If the interest is at the rate of 4% compounded annually,
then the payment due in two years is
7)
A)
$1155.43.
B)
$1203.14.
C)
$1000.00.
D)
$1191.00.
E)
$1118.46.
8)
Consider the following annuity: $2000 due at the end of each year for two years, and $3000 due
thereafter at the end of each year for three years. At an interest rate of 4% compounded annually,
the present value of the annuity is
8)
A)
$11,469.37.
B)
$10,211.37.
C)
$12,487.24.
D)
$10,541.31.
E)
$9,583.28.
9)
Suppose $500 is initially placed in a savings account that earns interest at the rate of 8%
compounded semiannually. Thereafter, $500 is deposited in the account at the end of every six
months for five years. The value of the account at the end of five years is
9)
A)
$4055.45.
B)
$4555.45.
C)
$6799.78.
D)
$6743.18.
E)
$6003.05.
10)
Suppose a company establishes a sinking fund to replace equipment that has a salvage value of
$50,000. The company deposits $20,000 into the fund at the end of every six months. If interest is
earned at the rate of 8% compounded semiannually, the value of the fund at the end of six years is
10)
A)
$250,516.10.
B)
$137,701.48.
C)
$237,701.48.
D)
$300,516.11.
E)
$187,701.48.
11)
An interest rate of 8% compounded semiannually corresponds to an effective rate of
11)
A)
9.2456%.
B)
12%.
C)
8.1600%.
D)
8%.
E)
8.2031%.
12)
An $800 loan is amortized by equal quarterly payments over two years. If interest is at the rate of
16% compounded quarterly, then the quarterly payment is
12)
A)
$104.16.
B)
$86.82.
C)
$132.14.
D)
$124.36.
E)
$118.82.
13)
If an investment of $20,000 earns interest at an annual rate of 9% compounded continuously, then
the value (in dollars) of the investment six years from now is
13)
A)
20,000(1.09)6
B)
e0.54
20,000
C)
20,000e–0.54
D)
20,000e0.54
E)
20,000(1.09)–6
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
14)
A company earns a profit of $2000 in its first month. Suppose its profit increases by 10%
each month for two years. Find the amount of profit the company earns in its sixth and
sixteenth months.
14)
15)
The population of a small town is growing at an effective rate of 2.1%. If the current
population is 53,000, what will the population be in 8 years?
15)
16)
If an initial investment of $4000 grows to $5718 in six years, find the nominal rate of
interest, compounded quarterly, that was earned by the money.
16)
17)
Given an interest rate of 7.25% compounded monthly, find the present value of the
following annuity: $700 at the end of each month for three years and $900 at the end of
each month for five more years.
17)
18)
To what sum will $1000 accumulate if it is invested at 10% compounded annually for one
year and then at 10% compounded semiannually for two years?
18)
19)
At what nominal rate of interest, compounded monthly, will an investment double in 15
years?
19)
20)
The population of a city grows from 110,000 to 116,600 in one year. If the city continues to
grow at that rate, find the number of years it will take for the population to double.
20)
21)
Suppose a person deposits $1000 in a savings account at the end of every six months. What
is the value of the account at the end of five years if interest is at a rate of 10% compounded
semiannually?
21)
22)
How much must be invested at an interest rate of 7.25% compounded quarterly to have
$10,000 in two years?
22)
23)
Suppose an initial investment grows from $12,000 to $30,000 over ten years. First find the
nominal rate compounded quarterly and then find the equivalent effective rate.
23)
24)
If $10,000 is invested at an effective rate of 4.25% for 8 years, what is the accumulated
amount?
24)
25)
To purchase land for an industrial site, a company agrees to pay $20,000 down and $10,000
at the end of every six–month period for 10 years. If the interest rate is 10% compounded
semiannually, what is the corresponding cash value of the land?
25)
26)
After putting $10,000 down on a piece of property, a woman began paying $2500 a quarter
for nine years. Given an interest rate of 7.75% compounded quarterly, how much would
the property cost if the woman had paid for it in cash?
26)
27)
A trust fund for a newborn is being set up by a single payment so that at the end of 18
years there will be $34,000. If the fund earns interest at the rate of 6.25% compounded
monthly, how much money should be paid into the fund initially?
27)
28)
Suppose you leave an initial amount of $315 in a savings account for 10 years. If interest is
compounded monthly, use a graphing calculator to graph the compound amount S as a
function of the nominal rate of interest. Determine the nominal rate of interest so that there
is $519 after 10 years.
28)
29)
You wish to be a millionaire when you retire. To accomplish this you decide to open up an
IRA and make equal monthly payments at the end of each month. If the IRA earns 7.5%
compounded monthly and you know you will retire in 40 years, what must be the monthly
payment to obtain your $1,000,000?
29)
30)
Find the present value of a future value of $325 due in 10 years at an A.P.R. of 5.3%
compounded semiannually.
30)
31)
Find the present value of an annuity of $200 per month for 71
2 years at an interest rate of
7% compounded monthly.
31)
32)
A trust fund for a 12–year–old child is being set up by a single payment so that when the
child is 21 there will be $24,000. If the fund earns interest at the rate of 7.25% compounded
quarterly, how much money should be paid into the fund initially?
32)
33)
At an annual rate of 8% compounded continuously, in how many years would it take for a
principal to double?
33)
34)
A company repays a $50,000 loan by paying 10% of the outstanding loan each month. Find
the amount the company pays in the fourth and twentieth months.
34)
35)
An investment grows from $600 to $642 in one year. If the investment continues to grow at
that rate, find the number of years it will take for the investment to double.
35)
36)
The premiums on an insurance policy are $80 every six months, payable at the beginning
of each six–month period. If the policy holder wishes to pay 1 year’s premiums in advance,
how much should be paid provided that the interest rate is 4.3% compounded
semiannually?
36)
37)
Determine the effective rate equivalent to an annual rate of 73
4% compounded
continuously.
37)
38)
Suppose the Laus wish to save $36,000 for a down payment in three years. If they make
payments at the end of every month into an account paying 7.5% compounded monthly,
what size payments should they make?
38)
39)
Suppose a woman purchases a building with an initial down payment of $40,000, and then
makes monthly payments: $1500 at the end of each month for four years and $2000 at the
end of each month for six more years. Given an interest rate of 5.5% compounded monthly,
find the present value of the payments and the list price of the building. (Round your
answer to the nearest dollar.)
39)
40)
What is the present value of an annuity of $1000 per month for ten years at an interest rate
of 6.3% compounded monthly?
40)
41)
You have a choice of two banks. One bank pays interest at 4.66% compounded 360 times a
year and the other bank pays interest at 4.65% compounded 365 times a year. Which is the
better choice?
41)
42)
A trust fund is to be set up by a single payment so that at the end of 10 years there will be
$1,000,000 in the fund. If interest is compounded continuously at an annual rate of 9%, to
the nearest dollar, how much money should be paid into the fund initially?
42)
43)
A rubber ball always bounces back 2
3 of its previous height. If the ball is thrown up to a
height of 30 feet, give the first five heights of the ball.
43)
44)
Cyndi bought a multimedia home computer system for $4500 and agreed to pay off the
loan by making monthly payments of $109. If the store charges an interest rate of 9.7%
compounded monthly, how many months will it take to pay off the debt?
44)
45)
If a person deposits $1000 in a savings account that pays an interest rate of r%
compounded continuously, and the account has $1400 at the end of 4 years, find the
interest rate.
45)
46)
Suppose you deposit $200 at the end of every month into a bank account that pays 6%
compounded monthly. After six years, how much will you have?
46)
47)
Given a payment of $800 per quarter for five years, use a graphing calculator to graph the
present value A as a function of the interest rate per quarter r. Determine the nominal
interest rate if the present value of the annuity is $14,000.
47)
48)
$200 is invested at the rate of 4.5% compounded semiannually for 8 years. Find the
compound amounts at the end of the 2nd, 4th, and 8th years.
48)
49)
Suppose an initial investment grows from $330 to $600 over five years. First find the
nominal rate compounded monthly and then find the equivalent effective rate.
49)
50)
If $4,200 is invested at an annual rate of 5.4% compounded monthly for 10 years, find the
compound amount.
50)
51)
A trust fund for a 8–year–old child is being set up by a single payment so that when the
child is 20 there will be $12,000. If the fund earns interest at the rate of 6.5% compounded
semiannually, how much money should be paid into the fund initially?
51)
52)
Suppose you leave an initial amount of $250 in a savings account for 20 years. If interest is
compounded daily (use 365 times per year), use a graphing calculator to graph the
compound amount S as a function of the nominal rate of interest. Determine the nominal
rate of interest so that the amount doubles after 20 years.
52)
53)
A company repays a $40,000 loan by paying 20% of the outstanding loan every four
months for five years and then pays off the rest. How much was the company’s final
payment?
53)
54)
Suppose Mr. Takegawa owes Ms. Perez three sums of money: $1000 due in 2 years, $1500
due in 5 years, and $2000 due in 8 years. Suppose he would rather pay her $2000 now and
the rest in 3 years. If the interest rate is 6% compounded annually, how much will he owe
in 3 years?
54)
55)
Suppose that you can invest $5000 in a business that guarantees you the following cash
flows: $3000 at the end of 2 years, $2000 at the end of 4 years, and $1500 at the end of 6
years. Use a graphing calculator to graph the net present value as a function of the interest
rate compounded annually. Determine the interest rate for which the investment is
profitable.
55)
56)
A debt of $1000 due 4 years from now and $1500 due 6 years from now, is instead to be
paid off by a single payment 5 years from now. How much is the payment if an interest
rate of 8.4% compounded monthly is assumed?
56)
57)
Find the future value of an annuity due with quarterly payments of $550 for 32 years at
3.75% compounded quarterly.
57)
58)
What is the present value of an annuity of $300 per quarter for five years at an interest rate
of 4.5% compounded quarterly?
58)
59)
Suppose that you can invest $11,000 in a business that guarantees you the following cash
flows: $5500 at the end of 2 years, $4500 at the end of 4 years, and $4000 at the end of 5
years. Assuming an interest rate of 6.25% compounded annually, find the net present value
of the cash flows. Is the investment profitable?
59)
60)
If $5,600 is invested at an effective rate of 2.1% for 17 years, what is the compound amount?
60)
61)
For an initial investment of $10,000, suppose a company guarantees the following cash
flows at the end of the indicated years:
Year Cash Flow
1$4000
3$8000
Assume an interest rate of 5% compounded annually. (a) Determine the net present value
of the cash flows. (b) Is the investment profitable?
61)
62)
Suppose you wish to purchase a factory that will yield an annual return of $12,000 for 12
years, after which the factory will have no value. You want to earn 8.25% annually on your
investment and also set up a sinking fund to replace the purchase price. If money is placed
in the fund at the end of each year and earns 4.2% compounded annually, how much
should you pay for the factory?
62)
63)
Given an annuity with equal payments at the end of each month for six years and an
interest rate of 5.3% compounded monthly, use a graphing calculator to graph the present
value A as a function of the monthly payment R. Determine the monthly payment if the
present value of the annuity is $30,000.
63)
64)
An initial investment of $240 grows at an annual rate of 5% compounded quarterly. Find
how long it takes for the investment to amount to $300.
64)
65)
Miguel has the opportunity to invest $3000 in a friend’s business such that he will be
repaid $4500 in six years. On the other hand, he can put the $3000 in a savings account that
pays 5.5% compounded quarterly. Which investment is better?
65)
66)
If $14,300 is invested at an A.P.R. of 8.25% compounded semiannually for 3 years, find a)
the compound amount, and b) the compound interest.
66)
67)
The Krishnans amortize a loan of $150,000 for a new home by obtaining a 40–year
mortgage at the rate of 10.2% compounded monthly. Find (a) the monthly payment, (b) the
total interest charges, and (c) the principal remaining after 15 years.
67)
68)
A woman makes house payments of $4200 at the beginning of every quarter. If the woman
wishes to pay 11
2 year‘s worth of payments in advance, how much should she pay
provided that the interest rate is 5.4% compounded quarterly?
68)
69)
Determine the effective rate equivalent to an annual rate of 10% compounded
continuously.
69)
70)
Find the present value of an annuity due with semiannual payments of $350 for 35 years at
6.25% compounded semiannually.
70)
71)
If $12,000 is used to purchase an annuity consisting of equal payments at the end of every
six months for the next 7 years and the interest rate is 6.2% compounded semiannually,
find the amount of each payment.
71)
72)
Determine the effective rate equivalent to an annual rate of 8% compounded continuously.
72)
73)
If $2,575 is invested at an A.P.R. of 7% compounded semiannually for 15 years, find the
accumulated amount.
73)
74)
At a car dealership, you are given two options for financing a new car worth $16,000.
Option 1: You can take out a 5 year loan at 0% A.P.R. compounded monthly, or Option 2:
You can get $3,000 cash back and finance the rest at 4.9% A.P.R. compounded monthly for
5 years. Which is the better option for you?
74)
75)
A ball rebounds 2
3 of its previous height after each bounce. If the ball is dropped from a
height of 27 feet, how far has it traveled in the air when it hits the ground for the twentieth
time?
75)
76)
An initial investment of $10,000 grows at an annual rate of 3.5% compounded monthly.
Find how long it takes for the investment to amount to $14,400.
76)
77)
If $25,000 is used to purchase an annuity consisting of equal payments at the end of each
year for the next 8 years and the interest rate is 5% compounded annually, find the amount
of each payment.
77)
78)
A debt of $2000 due four years from now is to be repaid by a payment of $1000 now and a
second payment at the end of two years. How much should the second payment be if the
interest rate is 5% compounded annually?
78)
79)
Suppose a diagnostic machine will yield a net of $1000 per quarter for 5 years, after which
the machine can be sold for $1000. How much should a firm pay for the machine if it wants
to earn 7.5% annually on its investment and also set up a sinking fund to replace the
purchase price? For the fund, assume quarterly payments and a rate of 5.5% compounded
quarterly.
79)
80)
What is the effective rate that corresponds to a nominal rate of 20% compounded
quarterly?
80)
81)
A person has the option of satisfying a debt by either paying $5000 now and $5000 in two
years, or by paying $3000 now, $3000 a year from now, and a final payment of x dollars
two years from now. Determine an equation of value that corresponds to the value of all
payments at the end of two years. It is not necessary to solve the equation. Assume that
interest is at the rate of 10% compounded semiannually.
81)
82)
Suppose that you want to invest some money in order to have $100 available at some later
time. If you invest it at 7% interest compounded continuously, the amount you need to
invest now, P, is related to the number of years from now that you need the money, t, by:
P(t) = 100e–0.07t. Graph this on your graphing calculator in the window 0,20 ×0,100
Discuss the behavior of this graph.
82)
83)
Find the sum of the geometric series: 1 +2
3+2
3
2
+2
3
3
+2
3
4
83)
84)
Given an interest rate of 4.6% compounded semiannually, find the present value of the
following annuity: $2100 at the end of every six months for six years and $3000 at the end
of every six months for four more years.
84)
85)
If $100 is invested at a rate of 5% compounded continuously, the amount in the account is
given by: S=100e0.05t. If the same principal is invested at an account earning 5%
compounded semiannually, the amount is given by: S= 100 ·1.0252x. Consider the
difference in these two investments by graphing both functions on your graphing
calculator and looking at the years 5 through 7. (Use the window
5, 7 ×128,142 .) What do you notice about the two graphs?
85)
86)
Find the present value of an annuity due with quarterly payments of $2,750 for 27 years at
7.8% compounded quarterly.
86)
87)
Over a period of 3 years, an original principal of $1000 accumulated to $1200 in an account
where the interest rate was compounded monthly. Determine the rate of interest to two
decimal places.
87)
88)
Suppose that you can invest $10,000 in a business that guarantees you the following cash
flows: $5000 at the end of 2 years, $4000 at the end of 4 years, and $3000 at the end of 6
years. Assuming an interest rate of 7.25% compounded annually, find the net present value
of the cash flows. Is the investment profitable?
88)
89)
Find the present value of an ordinary annuity with monthly payments of $125 for 10 years
at 4.5% compounded monthly.
89)
90)
James amortizes a loan of $210,000 for a new home by obtaining a 40–year mortgage at the
rate of 7.5% compounded monthly. Find (a) the monthly payment, (b) the total interest
charges, and (c) the principal remaining after 15 years.
90)
91)
Find the present value of a future value of $5,000 due in 7 years at a nominal rate of 3%
compounded quarterly.
91)
92)
A debt of $12,000, which is due 10 years from now, is instead to be paid off by four
payments: $3000 now, $2000 in 3 years, $2000 in 6 years, and a final payment at the end of
8 years. What would this payment be if an interest rate of 5.5% compounded semiannually
is assumed?
92)
93)
An investment grows from $10,240 to $10,700.80 in one year. If the investment continues to
grow at that rate, find the number of years it will take the investment to double.
93)
94)
Find the present value of $5000 due in 3 years if the interest rate is 63
4% compounded
monthly.
94)
95)
A bank pays 4% annual interest compounded quarterly. How large a deposit must be
made now in order that the account contains $1500 at the end of 3 years?
95)
96)
Suppose you can invest $10,000 at 4.5% compounded quarterly or at 4.7% compounded
annually. Which is the better choice and how much more per year would you earn?
96)
97)
Suppose Lena deposits $500 at the end of every month into a bank account that pays 5.4%
compounded monthly. After five years, how much will she have?
97)
98)
A person purchases a home for $130,000, makes a down payment of $30,000. Find the
monthly payment if the person takes a loan for 25 years with an interest rate of 8%
compounded monthly.
98)
99)
A couple bought a motorboat for $11,000 and agreed to pay off the loan by making
monthly payments of $559. If the dealer charges an interest rate of 8.9% compounded
monthly, how many months will it take to pay off the debt?
99)
100)
Suppose Lena deposits $500 at the beginning of every month into a bank account that pays
5.4% compounded monthly. After five years, how much will she have?
100)
101)
Determine the present value of $4000 due in 5 years if the interest rate is 10% compounded
semiannually.
101)
102)
Suppose you leave an initial amount of $320 in a savings account for 30 years. If interest is
compounded monthly, use a graphing calculator to graph the compound amount S as a
function of the nominal rate of interest. Determine the nominal rate of interest so that the
amount triples after 30 years.
102)
103)
$200 is invested at the rate of 6% compounded monthly for 5 months. List the compound
amounts at the end of each month as a geometric sequence.
103)
104)
An investment is compounded daily (use 365 times per year). Use a graphing calculator to
graph the effective rate, re , as a function of the nominal rate r. Then use the graph to find
the nominal rate that is equivalent to an effective rate of 5.4%.
104)
105)
An investment is growing at an effective rate of 12.4%. If the amount invested is currently
$12,000, what will the amount be in 6 years?
105)
106)
Suppose a machine will yield a net of $200 per month for 5 years, after which the machine
would be worthless. How much should the firm pay for the machine if it wants to earn 5%
annually on its investment and also set up a sinking fund to replace the purchase price?
For the fund, assume monthly payments and a rate of 4% annually.
106)
107)
Suppose that you want to invest some money in order to have $1000 available at some later
time. If you invest it at 7% interest compounded continuously, the amount you need to
invest now, P, is related to the number of years from now that you need the money, t, by:
P(t) = 1000e–0.07t. Graph this on your graphing calculator in the window 0,20 ×0,1000 .
Discuss the behavior of this graph.
107)
108)
Suppose you have the opportunity to invest $6000 in a business venture such that you will
be repaid $8000 in five years. On the other hand, you can put the $6000 in a savings
account that pays 5.25% compounded monthly. Which investment is better?
108)
109)
A person amortizes a loan of $180,000 for a new home by obtaining a 30–year mortgage at
the rate of 8.7% compounded monthly. Find (a) the monthly payment, (b) the total interest
charges, and (c) the principal remaining after 10 years.
109)
110)
Find the present value of an ordinary annuity with quarterly payments of $250 for 40 years
at 7.25% compounded quarterly.
110)
111)
Suppose you have the opportunity to invest $1000 in a business such that the value of your
investment after seven years will be $1500. On the other hand, you can put the $1000 into a
certificate of deposit that pays 6% compounded monthly. Which is better?
111)
112)
Find the future value of an ordinary annuity with quarterly payments of $300 for 30 years
at 7.5% compounded quarterly.
112)
113)
Find the future value of an annuity due with semiannual payments of $6,250 for 21 years at
4.25% compounded semiannually.
113)
114)
Find the present value of a future value of $4,650 due in 18 months at an effective rate of
4.55%.
114)
115)
Find the future value of an ordinary annuity with semiannual payments of $475 for 30
years at 6.15% compounded semiannually.
115)
116)
If an initial investment of $3000 grows to $18,000 in five years, find the nominal rate of
interest, compounded quarterly, that was earned by the money.
116)
117)
The function that gives the effective rate that corresponds to an annual rate of x interest
compounded continuously is y=ex– 1. Graph this on your graphing calculator in the
window 0,0.5 ×0,1 and discuss what the behavior means.
117)
118)
A man bought a stereo system for $3500 and agreed to pay off the loan by making monthly
payments of $79. If the store charges an interest rate of 11% compounded monthly, how
many months will it take to pay off the debt?
118)
119)
An investment grows from $5500 to $6105 in one year. If the investment continues to grow
at that rate, find the number of years it will take for the investment to triple.
119)
120)
If $3,100 is invested at a nominal rate of 6% compounded quarterly for 7 years, find a) the
compound amount, and b) the compound interest.
120)
121)
You have a choice of two banks. One bank pays interest at 5.54% compounded monthly
and the other bank pays interest at 5.53% compounded daily (365 times a year). Which is
the better choice? How much more would you make in one year if you deposited $1000?
121)