invest $1200 in a mutual fund that earns 4.5% interest per year. How much money is in the account if you invested when you were 19 and took the money out at 55?

Question

2.) How much interest did you earn on your $1,200 investment.

Answer 1

Amount = principal ( 1+ r)ⁿ

 

Amount = 1200 ( 1+ 4.5/100)^55-19

 

= 5852.85

Answer 2

Age 19 = $1200

Age 20 = $1200*1.045 (initial amount with 4.5% simple interest added to the initial investment)

Age 21 = ($1200*1.045)*1.045 (4.5% simple interest compounded)

Age 22 = ($1200*1.045)*1.045*1.045 (4.5% simple interest compounded again)

 

The money continues to compound in this fashion for each year. So, the final equation looks like

 

1) Age 55 = $1200*1.045exp(55-19) = $1200*1.045exp36 = $5852.85 (4.5% simple interest compounded for 36 years)

 

2) Interest earned = $5852.85-1200 = $4652.85

 

The answer assumes that you earn the 4.5% interest in the 55th year.

 

Going beyond your question, if you withdraw the interest each year (1200*4.5% =$54), then you end up with only $54*36 years = $1944 or an average interest rate of the original 4.5%. So, by compounding the interest year after year, you end up with a much higher average return, $4652.85/36 years = $129.25 per year averaged over the 36 years which is an annualized return of 10.8% ($129.25/$1200).