INTEREST, DISCOUNT
1. You have a short-term promissory note payable in 8 months. The
nominal value of the note is now 20,000.00 and the interest rate
guaranteed by this IOU is 8% p.a. One month later you will decide to sell
the promissory note in the market at discount rate of 9% p.a. How much
will you obtain from your short-term promissory note? How long must
you hold the IOU if you like to sell it at least for 20,000.00?
Solution:
a. FV = PV*(1+0.08*8/12) = 21,066.667
PV (after 1m) = 21,066.667*(1-0.09*7/12) = 19,960.67
b. 20000=21,066.667*(1-0.09*t)
t=0.562588077 6 months and 22 days
The correct answer is 240 days (8months) – 202 days = 38 days!
2. What will be the future value of invested 10,000.00 in 3 years, 5 months
and 24 days? Use the best form of interest from the investor´s
perspective. The interest rate is 6% p. a. (The interest period is one
quarter)
Solution:
FV = 10000*(1+0,06/4)^(4*3+1)*(1+0,06*(2/12+24/360)) =
12305,42
Note one Interest period = 3 months, for Simple interest is remaining 2
months (of 12) and 24 days (of 360)
3. How long must you keep 12,500.00 deposited at a bank with an interest
rate of 7.5% p. a., if you will obtain 21,040.544 at the end? Solve the
problem with respect to the maximization of utility. Interest period is
one year.
Solution:
21,040.544=12,500.00*(1+0,075)^t
t = ln(21040,544/12500)/ln(1,075) = 7.200191 years space for linear
interest (simple interest), we know that we do have 7 whole Interest
periods!
21040,544 = 12500*(1+0,075)^7*(1+0,075*t)
t = 0,19444 7 years, 2 months and 10 days (0,19444*12 =
2,3333/0,333*30 = 9,999)
4. What is the annually interest rate on your bank account if you will obtain
in eleven years from interest payment 122,452.9604 (only interest). You
put on your bank account 150,000.00 and the bank calculates interest
semiannually. Interest period is one year.
FV (150,000.00+122,452.9604) = PV (150,000.00*(1+r)^11
r = (272452,9604/150000)^(1/11)-1 = 0,055756 i.e. 5.58 % p. a.
5. Calculate the effective interest rate. The annually interest rate is 4% and
interest will be calculated on daily basis (360 times in one year).
re = ( 1 + 0,04/360)^360-1 = 4.081 % p. a.
Hopefully it will help…
I am very sorry, but I do not offer other extra examples for additional
points – there will be only 2 points for d(12) for next week.