Question

if a payment of $1000 was being paid at the end of every four months for a 10-year annuity, find (a) the present value and (b) the future value at an interest rate of 14% compounded quarterly.

Answer 1

To calculate the present and future values of an annuity payment of $1000 every four months for 10 years at a 14% interest rate compounded quarterly, we can use the annuity formulas by plugging in the effective quarterly interest rate and the number of payments.

Step-by-step explanation:

To find the present and future value of an annuity, we can use the formulas for the present value (PV) and the future value (FV) of annuities. The student is dealing with an ordinary annuity, where payments are made at the end of each period. Considering a 14% annual interest rate compounded quarterly, and a payment of $1000 every four months, we can calculate the present and future values for a 10-year annuity.

For the present value, we use the formula:
PV = PMT * [(1 - (1 + r)^{-n}) / r],
where PMT is the annuity payment, r is the quarterly interest rate, and n is the total number of payments. The future value is calculated using the formula:
FV = PMT × [((1 + r)^n - 1) / r].

The number of annuity payments over 10 years with quarterly compounding is 30 (three payments per year for ten years), and the effective quarterly interest rate is 14% divided by 4, which is 3.5% or 0.035 in decimal form. Applying these values, the annuity formulas will yield the present and future values of the payments.