Question

Bill Ivy receives an annuity of $1,000, payable once every two years. The annuity stretches out over 24 years. The first payment occurs two years from today. What is the present value of the annuity if the effective annual interest rate is 9%?

A. $4,650 B. $4,800 C. $5,000 D. $5,450 E. $6,050

Answer 1

Answer:

Correct answer is:

A. $4,650

Explanation:

We take 2 years as one period

Given:

Effective annual interest rate is = 9%

Effective interest rate for one period (of two year) = (1 + 9%) ² -1 = 18.81%

Number of periods = 24 / 2 = 12

Present value of annuity = Annuity * (1 - 1/(1 +r) ⁿ) r

Where r = rate of interest period and

n = number of periods

In this case:

PV =1000 * (1 - 1 / (1 + 18.81%) ¹²) /18.81%

=$4,644.31

Closest amount from options given = $4,650

As such option A is correct and other options B, C, D and D are incorrect.