8.12D Compound 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 different from simple interest, which is only calculated on the principal amount.

Front

What is the formula for calculating compound interest?

Back

The formula for calculating compound interest is A = P(1 + r)^t, where A is the total amount after time t, P is the principal amount, r is the annual interest rate (in decimal), and t is the number of years.

Front

In the formula A = P(1 + r)^t, what does P represent?

Back

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

Front

In the formula A = P(1 + r)^t, what does t represent?

Back

t represents the time the money is invested or borrowed for, measured in years.

Front

In the formula A = P(1 + r)^t, what does A represent?

Back

A represents the total amount of money accumulated after n years, including interest.

Front

In the formula A = P(1 + r)^t, what does r represent?

Back

r represents the annual interest rate (in decimal form). For example, 5% would be represented as 0.05.

Front

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

Back

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

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. For example, interest compounded monthly will yield more than interest compounded annually.

Front

What is the difference between compound interest and simple 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

If a loan of $500 is taken at an interest rate of 4% compounded annually, how much interest will be paid after 5 years?

Back

A = 500(1 + 0.04)^5 = $608.33, so the interest paid is $608.33 - $500 = $108.33.