# Explain how much it will cost in interest to pay a loan off in 5 years if compounded monthly.

The catalog of payments over a time period describing payments on principle and interest is called an amortization schedule. The amount of interest paid over the life of the loan depends on the payment made each term. It is common to calculate the minimum payment amount using the formula:

A = P * r / (1 - (1 + r)^-n)

where A is the payment, P is the loan principle, and r is the interest rate per period, and n is the total number of periods, i.e. 5*12 months in your question. Once this payment amount is known, then an amortization schedule may be constructed.

Say your loan is for $1000, and the payment is $20 per month, and the interest rate is 1%/month. Then the interest charge is $1000*.01 = $10. So, in the first payment, the bank gets $10 in interest; the remaining $10 goes to pay off your loan, so now you owe $990. Next month, you pay $100, and the bank gets $9.90, so now you owe $979.90. In this scenario, paying off the $1000 takes about 6 years, and the total interest paid is about $400.