Question

HI5002 Pre-recorded Tutorial Questions for Topic 3A

Question 1: You wish to have an investment that will bring about $20 000 in five years, and the rate of return is 8% per annum. Required:

a. In term of time value of money, what does the amount of $20,000 represent?

b. How much do you need to invest now if the rate is compounded annually (to the nearest dollar)?

c. If you have $20,000 now and put the sum into a bank account that pays 5% per year. How much money will you have in 6 years if the rate is compounded semi-annually, quarterly, monthly and daily (to the nearest dollar)?

Answer 1

a) 20,000 after 5 years is the future value of the sum invested now @8% pa.

b) M = Amount invested

20,000 = M * (1+0.08)^5

M = Amount invested = 20,000/1.08^5 = 13,611.66 ~ 13,612

c) R = 5%

T = 6 years

semi-annually compounded

r = R/2 = 2.5%

t = T*2 = 12

A = 20,000 * (1+r)^t

A = 26,898

quarterly compounded

r = R/4 = 1.25%

t = T*4 = 24

A = 20,000 * (1+r)^t

A = 26,947

monthly compounded

r = R/12 = 5/12%

t = T*12 = 72

A = 20,000 * (1+r)^t

A = 26,980

daily compounded

r = R/365 = 5/365%

t = T*365 = 2190

A = 20,000 * (1+r)^t

A = 26,996

Give a thumbs up if this helped :)