Interest help

Question

Luke decided to begin saving for retirement at the age of 32. He decided to deposit $70 at the end of each month in an IRA that pays 5% compounded monthly.

What will be his interest if he decides to retire at 65 years of age?

Answer 1

Hi Raven,

 

We're talking about an annuity here.

 

To determine the future value of the annuity

P = PMT [((1 + r)ⁿ - 1) / r]

P = future value

PMT = monthly payment = $70

r = monthly interest rate = .05/12 = .0041666  <---we divide by 12 because the interest is compounded monthly.

n = time = 33 years * 12 months per year = 396

 

Putting this together.

P = 70[(1+.0041666)³⁹⁶ - 1)/.00416666]

P = $70,377.90

 

So at the end of 33 years, the value of the investment would be $70,377.90

$70 * 33 years * 12 monthly payments = $27,720

 

The interest earned is the difference between the future value, P, and the amount invested.

70377.9 - 27720 = $42,657.90