Compound and Continuous Interest

Front

What is compound interest?

Back

Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods. It is calculated at the end of each compounding period.

Front

What is continuous compounding?

Back

Continuous compounding is the process of earning interest on an investment or loan at an infinite number of compounding periods, leading to the formula A = Pe^(rt), where A is the amount, P is the principal, r is the rate, and t is time.

Front

How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 6.5% becomes 0.065.

Front

What is the formula for calculating compound interest?

Back

The formula for compound interest is 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

If you invest $1,000 at an interest rate of 5% compounded annually, how much will you have after 3 years?

Back

A = 1000(1 + 0.05/1)^(1*3) = $1,157.63.

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

How do you calculate the total amount paid on a loan with compound interest?

Back

To calculate the total amount paid on a loan with compound interest, use the formula A = P(1 + r/n)^(nt) and subtract the principal from the total amount to find the interest paid.

Front

What is the effective annual rate (EAR)?

Back

The effective annual rate (EAR) is the interest rate on an investment or loan that is compounded over a year, taking into account the effects of compounding.

Front

How do you find the principal amount needed to reach a specific future value with continuous compounding?

Back

Use the formula P = A / e^(rt), where A is the future value, r is the interest rate, t is the time in years, and e is the base of the natural logarithm.

Front

What is the future value of an investment of $800 at 4% interest compounded continuously for 5 years?

Back

A = 800 * e^(0.04*5) = $977.12.