Compound/Exponential

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 annually?

Back

Compound interest is calculated using the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What is continuous compounding?

Back

Continuous compounding is the process of earning interest on an investment that is calculated and added to the principal continuously, rather than at discrete intervals. The formula is A = Pe^(rt), where e is Euler's number.

Front

What is the formula for calculating the future value of an investment with continuous compounding?

Back

The formula is A = Pe^(rt), where A is the amount of money accumulated after time t, P is the principal amount, r is the annual interest rate, and t is the time in years.

Front

If you invest $1,000 at an interest rate of 5% compounded annually for 10 years, what will be the total amount?

Back

A = 1000(1 + 0.05)^10 = $1,628.89.

Front

What does the term 'principal' refer to in finance?

Back

The principal is the initial sum of money borrowed or invested, before interest.

Front

How do you calculate the interest earned on an investment?

Back

Interest earned can be calculated by subtracting the principal from the total amount after interest is applied: Interest = A - P.

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 is the formula for calculating simple interest?

Back

The formula for simple interest is I = Prt, where I is the interest, P is the principal, r is the rate of interest per year, and t is the time in years.

Front

If a painting is worth $12,000 and appreciates at 8% per year, what will its value be after 5 years?

Back

Value = 12000(1.08)^5 = $17,600.64.