Question

Suppose you invest $210,000 in an annuity that returns 6 annual payments, with the first payment one year from now and each subsequent payment growing by 5%. At an interest rate of 8%, how much is the first annual payment you receive?

Answer 1

$40,510.82

Step-by-step explanation:

Present value = $210,000

Number of annual payments (n) = 6

Growth rate (g) = 5% or 0.05

Interest rate (r) = 8% or 0.08

Amount of first annual payment = [Present value * (r - g)] / [1 - {(1 + g)/(1 + r)}^n]

Amount of first annual payment = [210,000 * (0.08-0.05)] / [1 - [(1+0.05) / (1+0.08)]^6]

Amount of first annual payment = [210,000*0.03] / [1 - (0.972222)^6]

Amount of first annual payment = 6,300 / [1 - 0.844486]

Amount of first annual payment = 6,300 / 0.155514

Amount of first annual payment = 40510.82217678151

Amount of first annual payment = $40,510.82

So, the amount of the first annual payment you will receive is $40,510.82.