Question

Suppose you invest $250,000 in an annuity that returns 5 annual payments, with the first payment one year from now and each subsequent payment growing by 6%. At an interest rate of 7%, how much is the first annual payment you receive

Answer 1

$54,508.98

Step-by-step explanation:

Formula of present value of growing annuity: PVGA = A*[(1 - (1+g)^n/(1+i)^n)) / (i-g)

$250,000 = A*[(1 - (1+0.06)^5/(1+0.07)^5)] / (0.07 - 0.06)

$250,000*(0.01) = A*(1 - (1.06)^5/(1.07)^5)

$250,000*(0.01) = A*(1 - 0.9541363)

$2500 = A * 0.045864

A = $2,500 / 0.045864

A = 54508.983080412

A = $54,508.98

So, the amount of the first annual payment i will receive $54,508.98.