Suppose that you invest R 13 000 for 8.25 years into a fund promising the following returns:
4% p.a. compounded weekly for the first 546 days.
12% p.a. compounded quarterly for the next 21 months.
9 % p.a. compounded monthly for the next 5 years.
Assuming 52 weeks in a year, what will the value of the fund be at maturity?
To calculate the future value of the investment, we need to calculate the value of each portion of the investment separately and then combine them.
1. For the first portion invested at 4% p.a. compounded weekly for the first 546 days:
- Interest rate (r) = 4%/52 = 0.0769% per week
- Time (t) = 546 days = 546/7 = 78 weeks
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the future value, P is the initial investment, r is the interest rate per period, n is the number of compounding periods per year, and t is the number of years.
A1 = 13,000(1 + 0.000769/1)^(1*78)
A1 = 13,000(1.000769)^78
A1 = 13,000 * 1.082236
A1 = R 14,071.09
2. For the second portion invested at 12% p.a. compounded quarterly for the next 21 months:
- Interest rate (r) = 12%/4 = 3% per quarter
- Time (t) = 21 months = 21/3 = 7 quarters
A2 = 14,071.09(1 + 0.03/1)^(1*7)
A2 = 14,071.09(1.03)^7
A2 = 14,071.09 * 1.239795
A2 = R 17,454.97
3. For the third portion invested at 9% p.a. compounded monthly for the next 5 years:
- Interest rate (r) = 9%/12 = 0.75% per month
- Time (t) = 5 years = 5*12 = 60 months
A3 = 17,454.97(1 + 0.0075/1)^(1*60)
A3 = 17,454.97(1.0075)^60
A3 = 17,454.97 * 1.549931
A3 = R 27,013.27
Therefore, the value of the fund at maturity will be R 27,013.27.