8.4 Practice - Compound Interest LATE2

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

The formula for annual compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years the money is invested or borrowed.

Front

What is the difference between annual and continuous compounding?

Back

Annual compounding calculates interest at the end of each year, while continuous compounding calculates interest at every possible moment, leading to a higher amount due to the formula A = Pe^(rt), where e is Euler's number.

Front

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

Back

$9,265.52

Front

If $4,000 is invested at 4.2% interest, compounded continuously, for 30 years, what is the ending balance?

Back

$14,101.70

Front

What is the formula for calculating the future value of an investment compounded monthly?

Back

The formula is A = P(1 + r/n)^(nt), where n is 12 for monthly compounding.

Front

How much will $15,000 grow in 8 years at 3.5% interest compounded monthly?

Back

$19,838.90

Front

What is the formula for calculating the future value of an investment compounded weekly?

Back

The formula is A = P(1 + r/n)^(nt), where n is 52 for weekly compounding.

Front

If Caiden earned $475 and deposited it at 3.8% interest compounded annually, what will be his balance after 15 years?

Back

$831.10

Front

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

Back

$2,222.81