To find the amount of the annual payment, we can use the formula for calculating the present value of an annuity:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = Present value of the annuity (R 85 000)
PMT = Payment amount per period (what we need to find)
r = Interest rate per period (8% p.a. compounded annually = 0.08)
n = Number of periods (17 years)
Substitute the given values into the formula:
85000 = PMT * [(1 - (1 + 0.08)^-17) / 0.08]
85000 = PMT * [(1 - (1.08)^-17) / 0.08]
85000 = PMT * [(1 - 0.206697) / 0.08]
85000 = PMT * (0.793303 / 0.08)
85000 = PMT * 9.9162875
PMT ≈ 85000 / 9.9162875
PMT ≈ 8556.39
Therefore, the investor will receive an annual payment of approximately R 8556.39 from the trust fund.
onsider 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?
1 answer