Question

A small business operator, Ms Smart, with limited investment opportunities deposits R10,000 into an investment account paying 6% annual interest and

leaves it on deposit for exactly 8 years. How much would be in the account at the end of 8 years if interest is compounded as follows

i. monthly                                                                                                                                                                                                                              [4 marks]

ii. semi-annually                                                                                                                                                                                                                   [4 marks]

iii. Calculate the effective annual rate (EAR) for (i) and (ii)                                                                                                                                        [6 marks]

iv. Based on your findings in parts (i) to (iv), what is the general relationship between frequency of compounding and the EAR?             [4 marks]

Answer 1

Deposit Amount = 10,000

Annual Interest rate = 6%

Monthly interest rate = 6%/12 = 0.5%

Semi-annual interest rate = 6%/2 = 3%

Tenure of Deposit = 8 years

No of months = 8*12 = 96 months

No of Semi-annual periods = 8*2 = 16 semi-annual periods

.

Part-1)

Amount that would be in the account at the end of 8 years if interest is compounded monthly:

= 10,000*(1.005^96)

= 10,000*1.614143

= $16,141.43

.

.

Part-2)

Amount that would be in the account at the end of 8 years if interest is compounded semi-annually:

= 10,000*(1.03^16)

= 10,000*1.604706

= $16,047.06

.

.

Part-3)

Effective interest rate for (1) = (1.005^12) – 1

= 1.005^12 – 1

= 1.061678 – 1

= 0.061678

= 6.17%

.

Effective interest rate for (2) = (1.03^2) – 1

= 1.0609 – 1

= 0.0609

= 6.09%

Part-4)

General relationship between frequency of compounding and the EAR is that they have a direct relationship…i.e higher the frequency of compounding higher is the EAR.