You borrow $3000 from the bank at 2% annual interest compounded monthly. The monthly payment is $150. What is the balance after the third payment?

Answer 1

Let's first look at this problem from a hands on approach.

You Borrow $3000

At the end of one month you owe interest on the $3,000 borrowed..

Multiply the principal $3,000 by the monthly rate of interest which is 0.02/12 = .00166667, the interest is $5

You now owe the $3000 borrowed plus $5 interest

At this point you make the first payment of $150. Your balance becomes $3,000 + $5 - $150 = $2,855

Repeating the process in the second month starting with a balance of $2,855

You will owe at the end of the month $2,855 + .00166667*$2,855 = $2,859.76

Then making your 2nd $150 payment the new balance is $2,859.76 - $150 = $2,709.76

Repeating the process in the third month starting with a balance of $2,709.76

The calculation would be $2,709.76 + .0166667* $2,709.76 - $150 = $2,564.28

Final answer is $2,564.28

Or apply this formula

where B is the balance after n payments, A is the amount of the loan, i is the interest rate (per month), and P is the payment amount per month.

Answer 2