Question

Suppose that the effective annual interest rate is 4%. Find the present value and the accumulated value of the annuity-immediate consisting of the following 29 annual payments: $500, $600, ..., $1,800, $1,900, $1,800, ..., $600, $500.

a) Present value: $13,979.54; Accumulated value: $18,076.12
b) Present value: $15,238.24; Accumulated value: $20,176.40
c) Present value: $12,345.67; Accumulated value: $16,789.01
d) Present value: $14,567.89; Accumulated value: $18,901.23

Answer 1

The present and accumulated values of the annuity with annual payments ranging from $500 to $1,900 are calculated using the formulas for present and future value of annuities, considering a 4% interest rate and a 29-year term.

Step-by-step explanation:

The present value and accumulated value of the annuity-immediate with an effective annual interest rate of 4% and 29 annual payments increasing from $500 to $1,900 and then decreasing back to $500 can be determined through present value and future value formulas for annuities. An annuity-immediate entails that the payments are made at the end of each period; in this case, yearly.

To find the present value, each payment is discounted back to the present using the formula $Payment / (1 + interest rate)number of periods. As for the accumulated value, each payment is compounded to the end of the term using the formula $Payment * (1 + interest rate)number of periods until the end. By adding all these values, we can determine the total present value and accumulated value of the annuity.