Math problem

Question

Imagine investing $200 monthly into a 401(k) retirement account that averages an APR of 3.00% compounded monthly. You do this consistently for 45 years until retirement. Use the savings plan formula to calculate your final balance (future value). After this calculation, find how much of this future value is principal and how much is interest.

 
1) Final Balance: ????    (Round to the nearest dollar and do not use commas.)
 
2) Principal:  ???/(Round to the nearest dollar and do not use commas.)
 
3) Interest: ????(Round to the nearest dollar and do not use commas.)

Answer 1

This is a great question that shows how compound interest can stack up over time!

In order to do this one you want to set up the savings plan formula

FV = PMT * (((1 + rate)^n – 1) / rate)

Plugging in the values that we know this becomes

FV = 200 * (((1 + 0.03/12)^(12*45) – 1) / (0.03/12))

Both the rate and number of periods (n) in that formula have to be adjusted to months … the rate is 0.03/12 to convert the annual rate into a monthly rate. And then the number of years is 12*45 to convert over into months.

Plugging that expression into a calculator being mindful of the parentheses yields $228,074.59 for the final balance.

To break that up into the principal and interest then you want to think in terms of the amount that was invested. So the principal would be $200 * 12 * 45 = $108,000

Meaning that the interest would be the difference between the principal and future value.

$228,074.59 - $108,000 = $120,074.59

I hope that helps!

Kyle