120)
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.
120)
121)
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?
121)
122)
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?
122)
123)
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.
123)
124)
Given that the effective rate is 9%, determine the interest rate r which is compounded
continuously to give an effective rate of 9%.
124)
125)
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 15 years with an interest rate of 8%
compounded monthly.
125)
126)
A person establishes the following retirement plan: an immediate deposit of $10,000 and
quarterly payments of $1,500 at the end of each quarter into a savings account that earns
5% compounded quarterly, what is the amount of the investment after 21 years?
126)
127)
Find the future value of an annuity due with monthly payments of $250 for 26 years at 6%
compounded monthly.
127)
128)
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?
128)
129)
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.
129)
130)
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?
130)
131)
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?
131)
132)
The premiums on an insurance policy are $20 a month, payable at the beginning of each
month. If the policy holder wishes to pay 1 year’s premiums in advance, how much should
be paid provided that the interest rate is 5.1% compounded monthly?
132)
133)
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.
133)
134)
Suppose an annuity due consists of 6 yearly payments of $200 and the interest rate is 5%
compounded annually. Determine (a) the present value and (b) the future value at the end
of 6 years.
134)
135)
Suppose a corporation pays $50,000 for a machine that has a useful life of eight years and a
salvage value of $5000. A sinking fund is established to replace the machine at the end of 8
years. The replacement machine will cost $70,000. If equal payments are made into the
fund at the end of every 6 months and the fund earns interest at the rate of 10%
compounded semiannually, what should each payment be?
135)
136)
A man purchased a new laser printer for his computer for $1100 and agreed to pay off the
loan by making monthly payments of $59. If the store charges an interest rate of 12.2%
compounded monthly, how many months will it take to pay off the debt?
136)
137)
If $10,000 is invested at an effective rate of 4.25% for 8 years, what is the accumulated
amount?
137)
138)
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.
138)
139)
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?
139)
140)
Suppose an initial investment grows from $220 to $600 over fifteen years. First find the
nominal rate compounded monthly and then find the equivalent effective rate.
140)
141)
Suppose you can invest $6000 at 6.2% compounded monthly or at 6.5% compounded
semiannually. Which is the better choice and how much more per year would you earn?
141)
142)
Suppose you invest an initial amount of $10,000 at an annual rate of 8.2% compounded
monthly. Use a graphing calculator to graph the compound amount S as a function of the
interest periods. Determine how long it takes for the investment to accumulate to $22,500.
142)
143)
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.
143)
144)
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.
144)
145)
A debt of $600 is due 3 years from now and $800 due 5 years from now, is instead to be
paid off by two payments: $500 now and a final payment at the end of 6 years. What
would this payment be if an interest rate of 6% compounded quarterly is assumed?
145)
146)
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?
146)
147)
Determine the present value of $4000 due in 5 years if the interest rate is 10% compounded
semiannually.
147)
148)
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?
148)
149)
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.
149)
150)
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?
150)
151)
Determine the effective rate equivalent to an annual rate of 73
4% compounded
continuously.
151)
152)
Find the future value of an annuity due with semiannual payments of $6,250 for 21 years at
4.25% compounded semiannually.
152)
153)
After putting $20,000 down on a piece of property, a man began paying $500 a month for
ten years. Given an interest rate of 8% compounded monthly, how much would the
property cost if the man had paid for it in cash?
153)
154)
Find the present value of a future value of $4,200 due in 11 years at a nominal rate of 6%
compounded monthly.
154)
155)
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.
155)
156)
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?
156)
157)
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?
157)
158)
Mary amortizes a loan of $80,000 for a new home by obtaining a 15–year mortgage at the
rate of 9.9% compounded monthly. Find (a) the monthly payment, (b) the total interest
charges, and (c) the principal remaining after 8 years.
158)
159)
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.
159)
160)
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?
160)
161)
Find the sum of the geometric series: 1 +2
3+2
3
2
+2
3
3
+2
3
4
161)
162)
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%.
162)
163)
Find the present value of an ordinary annuity with monthly payments of $125 for 10 years
at 4.5% compounded monthly.
163)
164)
A $5000 loan is to be repaid over three years by equal payments due at the end of every
quarter. If interest is at the rate of 20% compounded quarterly, determine (a) the quarterly
payment and (b) the total interest paid.
164)
165)
At what nominal rate of interest, compounded quarterly, will an investment double in 15
years?
165)
166)
Suppose that you can invest $8000 in a business that guarantees you the following cash
flows: $4000 at the end of 2 years, $3500 at the end of 4 years, and $2000 at the end of 7
years. Use a graphing calculator to graph the net present value as a function of the interest
rate compounded annually. Determine the interest rates for which the investment is
profitable.
166)
167)
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.
167)
168)
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.
168)
169)
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.
169)
170)
Find the future value of an annuity due consisting of payments of $100 paid at the
beginning of each quarter for five years at the rate of 5% compounded quarterly.
170)
171)
A company repays a $50,000 loan by paying 10% of the outstanding loan each month. How
much has the company paid back after two years?
171)
172)
Find the present value of a future value of $4,650 due in 18 months at an effective rate of
4.55%.
172)
173)
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?
173)
174)
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?
174)
175)
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?
175)
176)
If $1000 is deposited into a savings account that earns interest at an annual rate of 6%
compounded continuously, find the value of the account at the end of seven years. Give
your answer to the nearest dollar.
176)
177)
An initial investment of $300 grows at an annual rate of 4.5% compounded bimonthly.
Find how long it takes for the investment to amount to $450.
177)
178)
Find the amount of an annuity consisting of payments of $100 paid at the end of each
quarter for five years at the rate of 5% compounded quarterly. Also find the compound
interest.
178)
179)
At what nominal rate of interest, compounded semiannually, will an investment double in
20 years?
179)
180)
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?
180)
181)
Find the present value of an annuity due with semiannual payments of $350 for 35 years at
6.25% compounded semiannually.
181)
182)
Find the amount of an annuity of payments of $150 at the end of every month for 3 years at
the rate of 4% compounded monthly. Also find the compound interest.
182)
183)
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.
183)
184)
What is the effective rate that corresponds to a nominal rate of 20% compounded
quarterly?
184)
185)
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?
185)
186)
An initial investment of $2600 grows at an annual rate of 7.5% compounded monthly. Find
how long it takes for the investment to amount to $3500.
186)
187)
If $30,000 is used to purchase an annuity consisting of equal payments at the end of each
quarter for the next 5 years and the interest rate is 8% compounded quarterly, find the
amount of each payment.
187)
188)
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.
188)
189)
A house worth $150,000 ten years ago has increased in value at an effective rate of 3% due
to inflation. Find the current value of the home.
189)
190)
You have two investment opportunities. You can invest $6000 at 12% compounded
monthly or you can invest $6100 at 12.1% compounded quarterly. Which has the better
effective rate of interest? Use a graphing calculator to graph both amounts as a function of
time in years. Which is the better investment over twenty years?
190)
191)
Find the present value of an ordinary annuity with semiannual payments of $450 for 30
years at 6% compounded semiannually.
191)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the value.
192)
s
11 0.03
192)
11.464
B)
14.192
46.141
12.808
Determine the first five terms of the geometric sequence.
193)
a1=6, r = – 5
193)
6, 1, –4, –9, –14
6, 30, 150, –750, 3750
6, –30, 150, –750, 3750
–5, –30, 150, –750, 3750
Find the value.
194)
a
31 0.04
194)
32.412
B)
17.292
17.874
17.588
Determine the first five terms of the geometric sequence.
195)
a1=6, r =5
195)
6, 11, 16, 21, 26
6, 30, 150, 750, 3750
30, 150, 750, 3750, 18,750
5, 30, 180, 1080, 6480
Find the value.
196)
a
60.03
196)
6.230
B)
5.417
61.249
4.580
197)
s
19 0.03
197)
26.87
B)
23.414
25.117
58.45
198)
a
31 0.09
198)
10.343
B)
10.406
11.879
10.274
199)
The Finance Club would like to endow an annual prize of $150 to the student who shows the most
promise as a future stockbroker. The club is confident that it can invest indefinitely at an interest
rate of at least 5% a year. How much does the club need to endow its prize?
199)
$3000
B)
$300
$3150
$158
Find the value.
200)
s
17 0.13
200)
53.739
B)
46.672
61.431
61.725
201)
a1=2, r =1
5
201)
2
5, 2
25 , 2
125, 2
625, 2
3125
2, 2
5, 2
25 , 2
125, 2
625
2, 11
5, 12
5, 13
5, 14
5
2, 10, 50, 250, 1250
Find the present value of the given perpetuity.
202)
$50,000 per year at the rate of 10% yearly
202)
$5,000,000
B)
$55,000
$500,000
$5,000
Find the limit.
203)
lim
n
n2+ 2n
2n2– 2n + 1
203)
1
B)
2
3
1
3
1
2
Find the value.
204)
s
10 0.07
204)
11.978
B)
13.816
28.102
15.784
30
Answer Key
31
Answer Key
32
Answer Key
33
Answer Key