#1. Suppose you owe $1,000 on a loan and the interest rate you are charged is 20% per year compounded annually. If you didn’t pay anything off, at this interest rate, how many years would it take for the amount you owe to double?
In finance, the “rule of 72” is a method for estimating an investment’s doubling time. The “rule” number (in this case 72) is divided by the interest percentage per period to obtain the approximate number of periods (usually years) required for doubling. So 72 divided by 20 (percentage of loan) equals 3.6 years.
#2. A 15-year mortgage typically requires higher monthly payments than a 30-year mortgage but the total interest over the life of the loan will be less.
Assuming the same interest rate for both loans, you will pay less in interest over the life of a 15-year loan than you would with a 30-year loan because you repay the principal at a faster rate. That’s why the monthly payment for a 15-year loan is higher. Let’s say you get a 30-year mortgage at 6 percent on a $150,000 home. You will pay $899 a month in principal and interest charges. Over 30 years, you will pay $173,757 in interest alone. But a 15-year mortgage at the same rate will cost you less. You will pay $1,266 each month but only $77,841 in total interest—nearly $100,000 less.
#3. Suppose you have $100 in a savings account earning 2 percent interest a year. After five years, how much would you have?
You’ll have more than $110 at the end of five years because your interest will compound over time. In other words, you earn interest on the money you save and on the interest your savings earned in prior years.