Question

QUESTION 5: Time value of money

5.1 You decided to invest R20 000 in a bank account over five years that is paying 5% interest per year. Calculate your interest if interest is compounded annually. Also, how much will you have accumulated if the interest was compounded monthly instead of annually?

5.2 Explain what a zero-coupon bond is and calculate the present value of the following zero-coupon bond with a par value of R100: The bond is to be redeemed in five years’ time and the interest is compounded semi-annually. The current market rate for such bonds is 8%.

Answer 1

5.1)

Future value = present value*(1+r)^n

r = rate of interest

n = number of periods

Annually:

future value = 20,000*(1+5%)^5 = 25,525.63

interest = 25,523.63 - 20,000 = R5,525.63

if compounded monthly:

r = 5% / 12 = 0.42%

n = 5*12 = 60

future value = 20,000*(1+0.42%)^60 = R25,667.17

Accumulated value = R25,667.17

interest = 25,667.17 - 20,000 = R5,667.17

5.2)

A zero coupon bond is a bond that does not pay any coupon during its time period and sells at a discounted price.it will pay par value at the time of maturity

using the same formula as above

r = 8% / 2 = 4%

n = 5*2 = 10

Current market rate = 100 / (1+4%)^10 = R67.56