Question

Mpumi Madonsela has recently qualified to be a Chartered Management Accountant and she is working at one of the big four accounting firms. Due to the limited salary of an article clerk, Mpumi did not contribute to any provident fund. Fortunately for her, the firm contributed to a pension fund on her behalf. She was not content with only a pension fund but was adamant that she wanted a provident fund to supplement her very extravagant life style.
Mpumi decided that on 1 January 2019, she would begin contributing to a selected provident fund. Her contributions towards this provident fund will be monthly in arrears. She wanted to get a lump sum pay-out on retirement date at the age of 65. Mpumi planned to put the lump sum in a money market account at a bank and withdraw a monthly amount for the rest of her life. The monthly amount must be an amount that will be able to maintain two and a half times her 1st year post article salary.
Additional information:
1. Mpumi will be turning 26 on 1 January 2019
2. Mpumi was signed off from her articles by CIMA on 1 January 2018. The accounting firm gave her a salary increase to R22 000 per month.
3. Currently the provident fund industry provide a return of 8% compounded monthly to try and be ahead of inflation.
4. Mpumi wants to contribute a maximum of R2 000 per month until she is 55 years old. Then the provident fund will invest the capital due to her at that stage in an interest bearing account until she retires. The provident fund guarantees that the interest bearing account will yield a 9% return compounded monthly.
5. The required return from retirement date onwards is expected to remain at 9% per annum.
REQUIRED:
a) Is the contribution that Mpumi wants to make sufficient to give her the monthly amount she requires after retirement? (12 Marks)
b) How much must Mpumi contribute to be able to have sufficient monthly payments after retirement? (10 Marks)
c) What would the effect on the monthly cash flows after retirement be if the bank compounded the investment semi-annually for the 10 year period in the interest bearing account? Using answer in (b). (6 Marks)
d) During the initial period when Mpumi will be contributing R2 000 per month, what is the effective rate that the provident fund delivers? (2 Marks)
e) If the interest bearing account yielded an effective interest rate of 9%, what would nominal rate, compounded quarterly, be? (2 Marks)

Answer 1

Answer:

Amount to be invested in amoney market fund post retirement is	= 55,000 * 12 / 9% = 7,333,333.33
Value of Capital at the age of 55 years, the period until Mpumi contributes is (i.e., Future Value (FV))	= 7,333,333.33/ (1+ 0.09)^10	PV of amount to be invested in a market fund post retirement @ 9%
Future Value (FV)	= 3,097,679
Period of Contribution	= 1/1/2019 to 31/12/2048	Since she is 26 years as on 1/1/2019 she will be 55 by 31/12/2048
Monthly Contribution (C)	$= \frac{FV}{[((1+i)^(n)-1)/i]*(1+i)}$	Here i = 8% /12 = 0.08/12 n = 29 years * 12 FV = 3,097,679 as calculated above
$= \frac{3,097,679.25}{[((1+0.08/12)^(29*12)-1)/0.08/12]*(1+0.08/12)}$
= 2,254.92

Therefore She has to contribute 2,254.92 per month in order to reach Mpumi Goal instead of 2,000