Question

David takes outs an annuity that we can he from after he retires in 20 years time he needs 3 000000 Rands in his annuity when he retires the bank gives him an interest rate of 10% compounded monthly calculate is monthly instalment into the fund if he starts paying immediately and thereafter at the end of each month until his last payment in 20 years.

Answer 1

R3912.89

Explanation:

You want the monthly deposit required to achieve an annuity value of R3,000,000 in 20 years with interest 10% compounded monthly, and the first payment made now. The last payment will be made in 20 years.

Value

The value is that of an ordinary annuity with 241 payments. The formula is ...

A = P(12/r)((1 +r/12)^241 -1)

where P is the monthly payment, r is the annual interest rate, and n is the number of payments.

Payment

Solving for P gives ...

P = A(r/12)/((1 +r/12)^n -1)

P = 3000000(0.10/12)/((1 +0.10/12)^241 -1) ≈ 3912.89

David's monthly payment should be R3912.89.

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Additional comment

An "ordinary annuity" usually assumes the first payment will be made at the end of the month. The last payment essentially earns no interest.

For an "annuity due", the payment is assumed made at the beginning of the month. The last payment earns one month's interest.

This problem uses features from both scenarios: the first payment is made at the beginning of the month, and the last payment is made at the end of the month. Effectively, there are 241 payments spanning 20 years, not just 240.

The payment is rounded up to R3912.89, so the final value is R0.67 more than R3,000,000.

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