Compound Interest and Continuously Compounded

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 different from Simple Interest?

Back

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

Front

What is the formula for Compound Interest?

Back

The formula for 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, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What does 'compounded continuously' mean?

Back

Compounding continuously means that the interest is calculated and added to the principal at every possible moment, leading to exponential growth.

Front

What is the formula for continuously compounded interest?

Back

The formula for continuously compounded interest 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 e is Euler's number (approximately 2.71828).

Front

If $400 is invested at a rate of 35% compounded continuously for 2 years, what is the ending balance?

Back

$805.50

Front

Which investment would yield a larger balance after 5 years: 4% compounded monthly or 3.9% compounded daily?

Back

4% compounded monthly (Option 1).

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 amount paid after 8 years for furniture costing $7,400 at 9.5% interest compounded quarterly?

Back

$15,683.28

Front

How does the growth rate of a population affect its size over time?

Back

A higher growth rate leads to a larger population size over time due to exponential growth.