1. You have accumulated $4,400 in credit card debt. Your credit card rate is 8.5% APR and you are charged interest every month on the unpaid balance on your account. How much interest must you pay every month, assuming the balance remains unchanged?

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HW 2 Solution
1. You have accumulated 4,400 in credit card
debt. Your credit card rate is 8.5 APR and you
are charged interest every month on the unpaid
balance on your account. How much interest must
you pay every month, assuming the balance remains
unchanged? 31.17 Interest 4,400(0.085/12)
31.17 2. You have accumulated 5,000 in credit
card debt. Your credit card rate is 9.5 APR and
you are charged interest every month on the
unpaid balance on your account. If you pay 500
a month and incur no new debt, how long will it
take you to pay off your credit card balance?
10.46 months P/Y12, I/Y9.5, PV5000, PMT-500
CPT,N N 10.46 months 3. Assume you want to
deposit 15,000 in a commercial bank. Which
savings account is better, one paying 6 with
yearly compounding or one paying 5.9 with
continuous compounding. Show your future value
calculations. 1st Option P/Y1, N1, I/Y6,
PV15000 CPT,FV FV 15,900 2nd Option FV
PVerT 15,000e0.059 (1) 15,911.63 Option 2
is better 4. If you need an estimated
250,000 for your kids college education in 7
years, how much money should you set aside today
on a U.S. savings bond earning 7.5 per year with
continuous compounding? PV FV/erT 250,000 /
e 0.075(7) 250,000 / 1.690459
147,888.84 5. You are being offered a 50,000
loan at a quoted rate of 5 with daily
compounding of interest. What is the nominal
rate? What is the periodic rate? What is the
effective rate? rnominal 5 rperiodic 5/365
0.01367 reffective (1 rnominal/m)m 1
(1 0.05/365)365 -1 1.051267 -1
5.1267 6. You are getting a 19,500 loan from
your bank to buy a car. You are required to pay
it within 5 years in monthly installments of
430.00 each due at month-end. What would the
periodic, nominal and effective rates be on this
loan? rnominal P/Y12, N60, PV19500, PMT -
430.00 CPT,I/Y, I/Y 11.6168 rperiodic
11.6168 /12 0.9681 reffective (1
0.116168/12)12 -1 (1.009681)12 1 1.122557 -
1 12.2557 7. You are getting a 3,000 loan
from a dealership to buy a used car. The dealer
has given you the choice between two different
credit alternatives. The first one is a two-year
financing deal, with payments of 142.60 per
month. The other one is a three-year financing
deal, with monthly payments of 100.83. Based on
effective rate of interest calculations, which of
the two loans in the previous question would you
chose? 1st Option P/Y12, N24, PV3000, PMT -
142.60 CPT,I/Y, I/Y 12.9819
reffective (1 0.129819 /12)12 1
(1.010818)12 1 1.137829 1 13.7829 2nd
Option P/Y12, N36, PV3000, PMT - 100.83
CPT,I/Y, I/Y 12.8256 reffective (1
0.128256 /12)12 1 (1.010688)12 1
1.136071 1 13.6071
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8. Your brother-in-law is inviting you to invest
some money with him. He argues that he can beat
whatever effective yield you are getting form
your mutual fund. He is asking you to invest
10,000 today and promises to pay you back
15,000 in five years. If your mutual fund pays
you an average annual rate of return of 8, is
your brother-in-law telling the truth? 8.4472
1) Find the total ROR over 5 years (15,000 -
10,000) / 10,000 50 2) Find the annual ROR
(1 RORTotal)1/T 1 (1 0.5)1/5 -1
(1.5)0.2 1 1.084472 1 8.4472
OR P/Y1, N5, PV-10,000, FV15,000 CPT I/Y
I/Y 8.4472 Your brother-in-law is telling the
truth
9. What is the future value of an ordinary
annuity yielding 6.00 APR that pays semiannual
payments of 500 for 1.5 years? (Do the math do
not use the financial functions on your
calculator. Draw a cash flow diagram) 1,545.45

FV PV(1 r/m)n PV(1 r/m)n-1 ..
500(1 0.06/2)2 500(1 0.06/2)1 500
500(1.06092 1.03 1) 500(3.0909)
1,545.45
FV ?
r 6
1 yr
0
1
2
3
PMT 500
10. You are considering financing a new car which
cost 48,999 with an amortized loan. Your bank
offers a nominal rate of 7.200 for a 6 year loan
with monthly payments. How much will each
payment be? (Draw a cash flow diagram) 840.10
Solution Opt 1 rperiodic rnominal / m
7.2/12 0.60 P/Y1, N72, I/Y0.6, PV48999
CPT,PMT PMT 840.10 Solution Opt 2 P/Y12,
N72, I/Y7.2, PV48999 CPT,PMT PMT 840.10
11. Today you deposit 2000 in a bank account
that pays 3.6 APR compounded weekly. How much
money would you have in that account 21 months
from now. Do not assume there are 4 weeks per
month. There are 52 weeks per year. 2,130.01
m 52, T 21 mos/12 mos per yr 1.75 n 52 x
1.75 91 P/Y52, N91, I/Y3.6, PV2000 CPT,FV
2,130.01
12. You are tasked with estimating the fair
market value of a security that promises uneven
future payments. The table below shows the
quarterly payment schedule (each cash flow occurs
at the end of the quarter). You consider 7.2
p.a. to be the appropriate opportunity cost.
What is the theoretical value of this security?
(Draw a cash flow diagram) 1,806.41
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
300 400 500 700
m 4 rperiodic rnominal 7.2/4 1.8 CF,
2nd, CLR WORK (Clears Cash Flow Registers) 0,
ENTER, ?, 300, ENTER ?, ?, 400, ENTER ?, ?, 500,
ENTER ?, ?, 700, ENTER NPV, 1.8, ENTER ?, CPT
1,806.41
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13. You are considering leasing a small warehouse
for 3 years. The lease requires monthly payments
of 448.00. Somewhere on the lease paperwork you
notice a statement to the affect that you will be
charged an nominal rate of 4.800. Ignore the
turn-in value or salvage value of the warehouse.
What is the value of the lease? (Draw a cash flow
diagram) 15,052.68
Solution Opt 1 rperiodic rsimple/m 4.8/12
0.4 Set to BGN mode, P/Y1, N36, I/Y0.4,
PMT448 CPT,PV PV 15,052.68 Solution Opt 2
Set to BGN mode P/Y12, N36 I/Y4.8, PMT448
CPT,PV PV 15,052.68
14. Fly By Night Trucking Company is financing a
new truck with an amortized loan of 50,000 to be
repaid in 11 semi-annual installments of
5,776.92, paid at the end of each six months.
(Draw a cash flow diagram) What type of annuity
is this?____________________. What is the annual
cost of debt for this loan? 8.4500
Ordinary Annuity or Annuity in Arrears Solution
Opt 1 1) P/Y1, N11, PV50000, PMT-5776.92
CPT,I/Y I/Y 4.225 This is a periodic rate! 2)
Find APR rnominal rperiodic x m 4.225 x 2
8.4500 Solution Opt 2 P/Y2, N11, PV50000,
PMT-5776.92 CPT,I/Y I/Y 8.4500
15. Today you deposit 90,000 of your company's
money in an investment account that pays 7.97
p.a. compounded weekly. How much money would you
have in that account 11 months from now? Do not
assume there are 4 weeks per month. There are 52
weeks per year. 96,815.98
m 52, T 11 mos/12 mos per yr 0.916667 yr n
52 per/yr x 0. 916667 yr 47.666667
periods P/Y52, N 47.666667, I/Y7.97, PV90000
CPT,FV 96,815.98
16. Today is 1 January and you plan to start
investing in a stock mutual fund that pays
quarterly dividends. The funds value has grown
at an average rate of 9.42 p.a. for the past 3
years. Today you deposited 1,500 into this
account and will continue to deposit that amount
at the beginning of every 3 months thereafter.
What type of annuity is this? _________________.
How much money would you have in this account
after 5 1/2 years? (Draw a cash flow diagram)
43,600.70
Annuity Due Solution Opt 1 rperiodic
rnominal/m 9.42/4 2.355 Set to BGN mode,
P/Y1, N22, I/Y2.355, PMT1500 CPT,FV FV
43,600.70 Solution Opt 2 Set to BGN mode
P/Y4, N22, I/Y9.42, PMT1500 CPT,FV FV
43,600.70
17. How many years will it take for your savings
account to accumulate 1m if it pays 4 interest
per year compounded semiannually and you deposit
10k every 6-months at the end of the 6-month
period? 27.74 years
a) Find number of periods rperiodic rnominal /
m 4/2 2 P/Y1, I/Y 2, PMT-10000,
FV1000000 CPT,N N 55.48 periods OR P/Y2,
I/Y 4, PMT-10000, FV1000000 CPT,N N 55.48
periods b) Find number of years Years N/m
55.48/2 27.74 years
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18. You are considering financing a new car which
with an amortized loan. Your bank offers a
nominal rate of 6.4500 for a 6 year loan with
monthly payments. You cannot afford to pay more
than 400 per month. What is the price of the
most expensive car you can afford to finance?
(Draw a cash flow diagram) 23,829.19
Solution Opt 1 rperiodic rnominal / m
6.45/12 0.5375 P/Y1, N72, I/Y0. 5375,
PMT400 CPT,PV PV 23,829.19 Solution Opt 2
P/Y12, N72, I/Y6.45, PMT400 CPT,PV PV
23,829.19
19. You are considering leasing a car that cost
34,000. The lease will be for 5 years and
requires monthly payments. Somewhere on the
lease paperwork you notice a statement to the
affect that you will be charged an APR of
5.4000. Assume the car will be worth 16,000 at
the end of the lease. How much will your
payments be? 413.13
rperiodic rnominal/m 5.4000/12 0.45 Set
BGN, P/Y1, N60, I/Y0.45, PV34000, FV -16000
CPT PMT PMT 413.13 OR Set BGN, P/Y12,
N60, I/Y5.4, PV34000, FV -16000 CPT PMT
PMT 413.13
20. Today you open a new investment account for
your company. The account has had an average
yield of 9.5600 p.a. over the last three years
and compounds every quarter. You plan to deposit
6,000 into this account every month, at the end
of the month. Your first deposit will be at the
end of this month. How much will you have in
this account 3 years from now?.
P/Y12, C/Y4, N36, I/Y9.56, PMT6000 CPT,FV
FV 248,737.32
OR Convert the quarterly rate
into a monthly rate then solve for FV 2nd ,
ICONV, 9.56, ENTER, ?, 4, ENTER, ?, CPT EFF
9.9082 ?, 12, ENTER. ?, CPT NOM
9.4848 P/Y12, N36, I/Y9.4848, PMT6000
CPT,FV FV 248,737.32