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

How is Compound Interest calculated?

Back

Compound Interest = P(1 + r/n)^(nt), where P = principal amount, r = annual interest rate (decimal), n = number of times interest applied per time period, t = number of time periods.

Front

What does 'compounded monthly' mean?

Back

It means that the interest is calculated and added to the principal every month.

Front

What is the formula for future value with continuous compounding?

Back

A = Pe^(rt), where A = amount of money accumulated after n years, including interest, P = principal amount, r = annual interest rate, t = time in years, e = Euler's number (approximately 2.71828).

Front

If you invest $1,000 at an interest rate of 5% compounded annually for 3 years, what is the future value?

Back

Future Value = 1000(1 + 0.05)^3 = $1157.63.

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

What does 'compounded semi-annually' mean?

Back

It means that the interest is calculated and added to the principal twice a year.

Front

How do you determine the number of compounding periods in a year?

Back

The number of compounding periods in a year is determined by how often interest is calculated and added to the principal (e.g., annually = 1, semi-annually = 2, quarterly = 4, monthly = 12, daily = 365).

Front

What is the effective annual rate (EAR)?

Back

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

Front

If a loan has an interest rate of 6% compounded quarterly, what is the effective annual rate?

Back

EAR = (1 + r/n)^(nt) - 1, where r = 0.06, n = 4, t = 1. EAR = (1 + 0.06/4)^(4*1) - 1 = 0.0614 or 6.14%.