Compound Interest Formula and Compounding Continuously

Front

What is the formula for compound interest compounded continuously?

Back

A = Pe^(rt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and t is the time the money is invested or borrowed for, in years.

Front

What does 'compounded annually' mean?

Back

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

Front

If you invest $1000 at an interest rate of 5% compounded annually, how much will you have after 3 years?

Back

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

Front

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

Back

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

Front

What is the difference between compound interest and simple interest?

Back

Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods, while simple interest is calculated only on the principal amount.

Front

How do you convert a percentage to a decimal for use in the compound interest formula?

Back

Divide the percentage by 100. For example, 5% becomes 0.05.

Front

What is the effect of increasing the compounding frequency on the amount of interest earned?

Back

The more frequently interest is compounded, the more interest will be earned, leading to a higher final amount.

Front

If Chelsea has $7500 in an account at 5% compounded continuously, how long will it take to grow to $10,643.01?

Back

Using the formula A = Pe^(rt), we find t = (ln(A/P))/r = (ln(10643.01/7500))/0.05 = 7 years.

Front

What is the formula for calculating the total amount paid on a loan with compound interest?

Back

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

Front

What is the principal amount in the context of compound interest?

Back

The principal amount is the initial sum of money that is invested or loaned.