Question

You believe you will need to have saved $470,000 by the time you retire in 30 years in order to live comfortably. If the interest rate is 7% per year, how much must you save each year to meet your retirement goal? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

HI

This question is on annuity problems.

Here Future Value FV= $470,000

Time t = 30 years

Interest Rate r= 7%

Yearly Payment P= ?

Here at first we will calculate present value of this future value of $470,000

Present Value PV = FV/(1+r)^t

PV = 470000/(1.07)^30 = $61,472.55

So each year saving formula

PV = P*(1-(1/(1+r)^t)/r

61472.55 = P*(1-(1/1.07^30)/0.07

61472.55*0.07 = P*0.8686

P = $4,975.61

Hence you will have to save $4,975.61 each year to have $470,000 after 30 years

Thanks