Compound Interest Assignment

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 continuously compounded interest?

Back

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

Front

If $5000 is invested at 3.75% compounded monthly for 25 years, what is the future balance?

Back

$12,749.30

Front

If $1,000 is invested at 16% interest compounded continuously for 5 years, what is the ending balance?

Back

$2,225.54

Front

What is the total interest paid on a loan of $1,690 at 5.7% compounded annually for 5.5 years?

Back

$602.45

Front

How do you find the initial amount if you know the final amount and the interest rate?

Back

Use the formula A = Pe^(rt) and solve for P: P = A / e^(rt).

Front

If Chelsea has $10,643.01 after investing $7500 at 5% compounded continuously, how long has the money been in the account?

Back

7 years

Front

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

Back

Increasing the compounding frequency results in more interest being earned, as interest is calculated and added to the principal more often.