You have an annuity which pays $1,200 every two years. The first payment is two years from now and the last payment is ten years from now. You can trade that annuity for another annuity of equivalent present value, which pays $180 per quarter starting today. The interest rate for both annuities is 4% per annum convertible quarterly. If you took the second annuity, how many quarterly payments would you receive? The last payment may be less than $180 but not more than $180.

31 payments

Explanation:

the present value of the first annuity is:

$1,200 / (1 + 1%)⁸ + $1,200 / (1 + 1%)¹⁶ + $1,200 / (1 + 1%)²⁴ + $1,200 / (1 + 1%)³² + $1,200 / (1 + 1%)⁴⁰ = $1,108.18 + $1,023.39 + $945.08 + $872.76 + $805.98 = $4,755.39

to determine the length of the second annuity:

PV = annuity payment x annuity factor

annuity factor = PV / annuity payment = $4,755.39 / $180 = 26.4188333

using an annuity table we must look for a present value annuity factor that corresponds to 1% interest rate and is close to 26.4188333

the annuity factor is between 30 and 31 payments. Since the final payment has to be less or equal to $180, we have to choose 31 payments.

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