Question

A couple received a $131,000 inheritance the year they turned 48 and invested it in a fund that earns 6.1% compounded semiannually. If this amount is deferred for 14 years (until they retire), how much will it provide at the end of each half year (in dollars) for the next 20 years after they retire

Answer 1

Answer:

It will provide an amount of $13,259

Explanation:

According to the given data we have the following:

present value of deferred annuity=$131,000

i=0.061/2=0.0305

n=20*2=40

k=14*2=28

Therefore, to calculate  how much will it provide at the end of each half year (in dollars) for the next 20 years after they retire we would have to calculate the following formula:

$131,000=R(1-(1+0.0305)∧-40/0.0305)*(1+0.0305)∧-28

$131,000=R(1-(1.0305)∧-40/0.0305)* (1.0305)∧-28

$131,000=R(1-0.3006/0.0305)* 0.4311

$131,000=R(22.93)*(0.4311)

R=$131,000/9.88

R=$13,259

It will provide an amount of $13,259