Question

Find the payment that you should be used for the annuity due whose future value is given. Assume that the compounding period is the same as the payment. 10,000; quarterly payments for 17 years; interest-rate 8% 

Answer 1

68.94

Explanation:

You want the quarterly payment for an annuity due that will have a value of 10,000 in 17 years if the interest rate is 8% compounded quarterly.

Annuity due

The payment for an annuity due is ...

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

where A is the future value, P is the payment, n is the number of compoundings per year and t is the number of years.

P = 10000(0.08/4)/(((1 +0.08/4)^(4·17) -1)(1 +0.08/4)) ≈ 68.94

The quarterly payment will be 68.94.

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Additional comment

An annuity due has payments made at the beginning of the period, so every payment earns a full period of interest.

This is in contrast to an ordinary annuity, which has the payments made at the end of the period. For an ordinary annuity, the last payment earns no interest, and the first payment does not earn any interest in the first period.

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