Question

Suppose you invest $290,000 in an annuity that returns 7 annual payments, with the first payment one year from now and each subsequent payment growing by 4%. At an interest rate of 6%, how much is the first annual payment you receive

Answer 1

The first annual payment of the growing annuity is $46,463.11

This is a case of a growing annuity, because each subsequent annual payment grows a rate of 4%.

The first annual payment can be determined using the present value formula of a growing annuity as provided  below:

PV=(C/r-g*)*(1-(1+g)^T/(1+r)^T))

PV=present value=amount invested=$290,000

C=first payment=the unknown

r=rate of return=6%

g=growth rate=4%

T=number of annual payments

$290,000=(C/6%-4%)*(1-(1+4%)^7/(1+6%)^7

$290,000=(C/0.02)*(1-0.875169790822493)

$290,000=C/0.02*0.124830209177507

$290,000*0.02=C*0.124830209177507

C=$290,000*0.02/0.124830209177507

C=first annual payment=$46,463.11

Find further guidance on present value of annuity in the link below:

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