A 25-year annuity is purchased for $650,000. Determine the payments it will deliver on a quarterly basis if the rate of interest is 5.05% compounded monthly.

Question

Quizplus · Accepted Answer

To find the quarterly payment, first convert the annual interest rate to a quarterly rate. The monthly rate is 5.05%/12 = 0.4208333%. Convert this to a quarterly rate: (1 + 0.004208333)^3 - 1 = 0.012662. Use the annuity formula: P = A * [(1 - (1 + r)^-n) / r], where P is the present value ($650,000), r is the quarterly rate (0.012662), and n is the total number of payments (25*4 = 100). Solving for A gives approximately $11,504.66.

A 25-Year Annuity Is Purchased for $650,000