Compound Interest Formula and Compounding Continuously

Front

What does 'quarterly' mean in terms of compounding frequency?

Back

4 times a year.

Front

What is the formula for compound interest when compounded continuously?

Back

A = Pe^{rt}, where A is the amount, P is the principal, r is the rate, and t is the time.

Front

If $3250 is invested at an interest rate of 6.2% compounded continuously for 8 years, what is the total amount?

Back

A = 3250e^{0.062 \cdot 8} = $3250e^{0.496} ≈ $3250 \times 1.640 = $5320.00.

Front

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

Back

The number of times interest is compounded per year.

Front

What is the formula for calculating the total amount with compound interest compounded annually?

Back

A = P(1 + r/n)^{nt}, where A is the 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

If a loan of $195,000 is taken at a 4% interest rate compounded annually for 30 years, how much will be paid back?

Back

$632,462.51.

Front

What is the effective annual rate (EAR) if the nominal rate is 6% compounded quarterly?

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%.

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 and also on the accumulated interest.

Front

How do you convert an interest rate from a decimal to a percentage?

Back

Multiply the decimal by 100.

Front

What is the principal amount if the total amount after 5 years at 5% interest compounded annually is $1,276.28?

Back

P = A / (1 + r)^t = 1276.28 / (1 + 0.05)^5 ≈ $1,000.