4.2 Compound Interest

Front

What is Compound Interest?

Back

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Front

What is the formula for calculating compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years.

Front

What does 'P' represent in the compound interest formula?

Back

'P' represents the principal amount, which is the initial sum of money invested or borrowed.

Front

What does 'r' represent in the compound interest formula?

Back

'r' represents the annual interest rate expressed as a decimal.

Front

What does 'n' represent in the compound interest formula?

Back

'n' represents the number of times that interest is compounded per year.

Front

What does 't' represent in the compound interest formula?

Back

't' represents the time the money is invested or borrowed for, in years.

Front

If $1,000 is invested at an interest rate of 5% compounded annually for 3 years, what is the total amount?

Back

A = 1000(1 + 0.05/1)^(1*3) = $1157.63.

Front

How does compounding frequency affect the total amount of compound interest earned?

Back

The more frequently interest is compounded, the more interest will be earned on the initial principal and accumulated interest.

Front

What is the difference between simple interest and compound interest?

Back

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal plus any interest that has already been added.

Front

What is the future value of an investment of $5000 at an interest rate of 3.75% compounded monthly for 25 years?

Back

A = 5000(1 + 0.0375/12)^(12*25) = $12,749.30.