Question #51276

A deferred annuity will pay you RM500 at the end of each year for 10 years,
however the first payment will not be made until three years from today (payments
will be made at the end of years 3 through 12). What amount will you have to deposit
today to fund this deferred annuity? Use an 8% discount rate and round your answer
to the nearest RM100.

Expert's answer

A deferred annuity RM500 (payments at the end of years 3 through 12), r = 8%.

To calculate the present value of a deferred annuity, you need to first use the present value formula for a regular annuity, which is as follows: C {[1 - (1 / ((1+i)^n)] / i}. In this formula, C represents the amount of each payment, i stands for interest rate and n stands for the number of payments. To obtain the present value of the deferred annuity, you only have to discount the previous figure according to the interest rate and the number of periods before the payments commence. You can do this using this formula: PV*[(1/(1+r))^t].

PV = 500*((1 - (1/(1.08^10))/0.08)/1.08^2 = 2876.41 - initial payment

To calculate the present value of a deferred annuity, you need to first use the present value formula for a regular annuity, which is as follows: C {[1 - (1 / ((1+i)^n)] / i}. In this formula, C represents the amount of each payment, i stands for interest rate and n stands for the number of payments. To obtain the present value of the deferred annuity, you only have to discount the previous figure according to the interest rate and the number of periods before the payments commence. You can do this using this formula: PV*[(1/(1+r))^t].

PV = 500*((1 - (1/(1.08^10))/0.08)/1.08^2 = 2876.41 - initial payment

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