Question

Steve Eckel recently set up a TDA to save for his retirement. He arranged to have $115 taken out of each of his biweekly checks; it will earn 9 7/8% interest. He just had his twenty-ninth birthday, and his ordinary annuity comes to term when he is 65. (Round your answers to the nearest cent.)

(a) Find the present value of the given annuity. $___.
(b) Interpret the present value of the given annuity.
You would have to invest a lump sum of ____$ now instead of $115 biweekly.

Answer 1

The present value of the given annuity is $74,503.10. This means that Steve Eckel would need to invest a lump sum of $74,503.10 now instead of $115 biweekly.

Step-by-step explanation:

Calculating the present value of an annuity involves determining how much money would need to be invested today to equal a series of future payments, given a specific interest rate. For Steve Eckel, who is saving for retirement with an annuity that will earn 9 7/8% interest, the present value calculation will show us the amount he would need to invest today to match the value of contributing $115 biweekly until he is 65, starting from his twenty-ninth birthday.

To find the present value of the given annuity, we can use the formula for the present value of an ordinary annuity:

Present Value = Payment * [(1 - (1 + interest rate)^(-n))/interest rate]

In this case, the payment is $115, the interest rate is 9.875% (or 0.09875 in decimal form), and the term is 35 years (65 - 29).

Using these values in the formula, the present value of the annuity is $74,503.10. This means that if Steve Eckel were to invest a lump sum of $74,503.10 now, he would have the same amount of money by the time he turns 65 as he would if he contributed $115 biweekly and earned 9 7/8% interest.