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CHEGG 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 :

Answer:

$40,511.23

Explanation:

This is a case of growing annuity and the amount invested in the annuity of $210,000 is the present value of the growing annuity, hence, using the present value formula of a growing annuity as shown thus

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

PV=$210,000

C=first annual payment=unknown

r=rate of return=8%

g=growing rate=5%

T=number of years that annual payments would be received=6

$210,000=C/8%-5%*(1-(1+5%)^6/(1+8%)^6))

$210,000=C/0.03*(1-(1+0.05)^6/(1+0.08)^6

$210,000=C/0.03*(1-(1.05)^6/(1.08)^6))

$210,000=C/0.03*(1-(1.3400956406/1.5868743229)

$210,000=C/0.03*0.1555124300

$210,000=C/0.03*0.1555124300

C=$210,000*0.03/0.1555124300

C=$40,511.23

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