Consider a trust fund of R 85 000. The conditions of the trust stipulate that for 17 years from the date that the trust fund is set up, one payment should be made in the beginning of each year to the investor. If this trust earns interest at a rate of 8% p.a. compounded annually, what is the amount of the annual payment that the investor will receive?
To calculate the annual payment that the investor will receive, we can use the formula for the future value of an annuity:
FV = Pmt * [(1 - (1 + r)^-n) / r]
Where:
FV = Future value of the annuity (R 85,000)
Pmt = Annual payment
r = Interest rate per period (8% or 0.08)
n = Number of periods (17 years)
85,000 = Pmt * [(1 - (1 + 0.08)^-17) / 0.08]
85,000 = Pmt * [(1 - 0.250905) / 0.08]
85,000 = Pmt * (0.749095 / 0.08)
85,000 = Pmt * 9.36367
Pmt ≈ R 9,081.46
Therefore, the annual payment that the investor will receive is approximately R 9,081.46.