150. Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The
terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would
you be paying in Year 2?
a.
$7,531
b.
$7,927
c.
$8,323
d.
$8,740
e.
$9,177
151. You are considering investing in a European bank account that pays a nominal annual rate of 18%,
compounded monthly. If you invest $5,000 at the beginning of each month, how many months would
it take for your account to grow to $250,000? Round fractional months up.
a.
23
b.
27
c.
32
d.
38
e.
44
N
37.16
Rounded up: 38
152. You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded
monthly. If you invest $3,000 at the end of each month, how many months will it take for your account
to grow to $150,000?
a.
39.60
b.
44.00
c.
48.40
d.
53.24
e.
58.57
I/YR
N
153. The store where you bought new home furnishings offers you two alternative payment plans. The first
plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly
payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate
is built into the monthly payment plan?
a.
12.31%
b.
12.96%
c.
13.64%
d.
14.36%
e.
15.08%
I/MO
Monthly annuity, so interest must be calculated on monthly basis
PMT
154. Your Green Investment Tips subscription is about to expire. You plan to subscribe to the magazine for
the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can
get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on
your funds and that the annual renewal rate will remain constant, how many years must you live to
make the lifetime subscription the better buy?
a.
7.48
b.
8.80
c.
10.35
d.
12.18
e.
14.33
155. You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded
quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another
$7,500 to the account two years (8 quarters) from now, how much will be in the account three years
(12 quarters) from now?
a.
$15,234.08
b.
$16,035.88
c.
$16,837.67
d.
$17,679.55
e.
$18,563.53
156. Partners Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid
quarterly. An offer to lend you the $50,000 also comes from Community Bank, but it will charge
6.0%, simple interest, with interest paid at the end of the year. What’s the difference in the effective
annual rates charged by the two banks?
a.
1.56%
b.
1.30%
c.
1.09%
d.
0.91%
e.
0.72%
157. Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of
each of the next 5 years. By how much would you reduce the amount you owe in the first year?
a.
$2,404.91
b.
$2,531.49
c.
$2,658.06
d.
$2,790.96
e.
$2,930.51
158. Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of
each of the next 5 years. How much would you still owe at the end of the first year, after you have
made the first payment?
a.
$10,155.68
b.
$10,690.19
c.
$11,252.83
d.
$11,845.09
e.
$12,468.51
159. Your older brother turned 35 today, and he is planning to save $7,000 per year for retirement, with the
first deposit to be made one year from today. He will invest in a mutual fund that’s expected to provide
a return of 7.5% per year. He plans to retire 30 years from today, when he turns 65, and he expects to
live for 25 years after retirement, to age 90. Under these assumptions, how much can he spend each
year after he retires? His first withdrawal will be made at the end of his first retirement year.
a.
$58,601
b.
$61,686
c.
$64,932
d.
$68,179
e.
$71,588
160. You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end
of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly,
what nominal annual interest rate will you be earning?
a.
7.62%
b.
8.00%
c.
8.40%
d.
8.82%
e.
9.26%
161. Your business has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but
with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the
repayment of principal?
a.
73.67%
b.
77.55%
c.
81.63%
d.
85.93%
e.
90.45%
162. On January 1, 2012, your sister’s pet supplies business obtained a 30-year amortized mortgage loan for
$250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the
interest paid for tax purposes. What will the interest tax deduction be for 2012?
a.
$17,419.55
b.
$17,593.75
c.
$17,769.68
d.
$17,947.38
e.
$18,126.85
163. You borrowed $50,000 which you must repay in 10 years. You plan to make an initial deposit today,
then make 9 more deposits at the beginning of each the next 9 years, but with the deposits increasing at
the inflation rate. You expect to earn 5% on your funds, and you expect a 3% inflation rate. To the
nearest dollar, how large must your initial deposit be to enable you to reach your $50,000 target?
a.
$3,008
b.
$3,342
c.
$3,676
d.
$4,044
e.
$4,448
2.
Formula approach:
1.941748% = (1 + I1572)/(1 + I1573) −1
constant dollar future target.
N = 10, I/YR = 1.941748, PV = 0, FV = −37204.70, and set to BEGIN mode.
$3,341.94 = PMT(H1593, I1570,0, −H1595,1)
Amount Needed (FV)
Inflation
164. Your 75-year-old grandmother expects to live for another 15 years. She currently has $1,000,000 of
savings, which is invested to earn a guaranteed 5% rate of return. If inflation averages 2% per year,
how much can she withdraw (to the nearest dollar) at the beginning of each year and keep the
withdrawals constant in real terms, i.e., growing at the same rate as inflation and thus enabling her to
maintain a constant standard of living?
a.
$65,632
b.
$72,925
c.
$81,027
d.
$89,130
e.
$98,043
165. Julian and Jonathan are twin brothers (and so were born on the same day). Today, both turned 25.
Their grandfather began putting $2,500 per year into a trust fund for Julian on his 20th birthday, and
he just made a 6th payment into the fund. The grandfather (or his estate’s trustee) will make 40 more
$2,500 payments until a 46th and final payment is made on Julian’s 65th birthday. The grandfather set
things up this way because he wants Julian to work, not be a “trust fund baby,” but he also wants to
ensure that Julian is provided for in his old age.
Until now, the grandfather has been disappointed with Jonathan and so has not given him anything.
However, they recently reconciled, and the grandfather decided to make an equivalent provision for
Jonathan. He will make the first payment to a trust for Jonathan today, and he has instructed his trustee
to make 40 additional equal annual payments until Jonathan turns 65, when the 41st and final payment
will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into
Jonathan’s trust today and each subsequent year to enable him to have the same retirement nest egg as
Julian after the last payment is made on their 65th birthday?
a.
$3,726
b.
$3,912
c.
$4,107
d.
$4,313
e.
$4,528
166. You plan to work for Strickland Corporation for 12 years after graduation and after that want to start
your own business. You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t =
6) and $15,000 annually for the following 6 years (t = 7 through t = 12). The first deposit will be made
a year from today. In addition, your grandmother just gave you a $25,000 graduation gift that you will
deposit immediately (t = 0). If the account earns 9% compounded annually, how much will you have
when you start your business 12 years from now?
a.
$238,176
b.
$250,712
c.
$263,907
d.
$277,797
e.
$291,687
167. You are in negotiations to make a 7-year loan of $25,000 to DeVille Corporation. To repay you,
DeVille will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of
Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4
through Year 7. You are confident the payments will be made, since DeVille is essentially riskless.
You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan. What cash flow
must the investment provide at the end of each of the final 4 years, that is, what is X?
a.
$4,271.67
b.
$4,496.49
c.
$4,733.15
d.
$4,969.81
e.
$5,218.30
168. Scott and Linda have been saving to pay for their daughter Casie’s college education. Casie just turned
10 at (t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses
at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year.
Ellen should graduate in 4 years⎯if she takes longer or wants to go to graduate school, she will be on
her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and
11).
So far, Scott and Linda have accumulated $15,000 in their college savings account (at t = 0). Their
long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4).
Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7.
They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and
7 be to cover Casie’s anticipated college costs?
a.
$1,965.21
b.
$2,068.64
c.
$2,177.51
d.
$2,292.12
e.
$2,412.76
1.
Determine the cost of each year during college and its PV at t = 8, discounted at the return
on investment.
Prior year (1 + infl) =
Known
values;
Cash flows:
$15,000.00
$5,000.00
We found the PV of the college costs (t = 8−11) at t = 8 above.
4.
Find the FV of t = 0 & 4 positive CFs at t = 8
Current college cost/year
Payments at t = 1, 2, 3, and 4
