Compound Interest Formula and Compounding Continuously

Front

What is the formula for compound interest compounded semi-annually?

Back

The formula is: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount (the initial amount of money), 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 does 'compounded continuously' mean in terms of interest calculation?

Back

Compounding continuously means that the interest is calculated and added to the principal at every possible moment. The formula used 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 (as a decimal), and e is Euler's number (approximately 2.71828).

Front

If Karla invested $1,000 at an interest rate of 6.75% compounded semi-annually, how would you express this in an exponential equation?

Back

The equation would be: A = 1000(1 + 0.0675/2)^(2*15).

Front

What does the variable 'r' represent in the compound interest formula?

Back

The variable 'r' represents the annual interest rate expressed as a decimal.

Front

How many times a year does interest compound if it is compounded quarterly?

Back

Interest compounds 4 times a year if it is compounded quarterly.

Front

What is the initial amount of money if the final amount is given by the formula A = 3250e^(0.062*8)?

Back

The initial amount of money deposited is $3250.

Front

Convert 6.5% to a decimal.

Back

6.5% as a decimal is 0.065.

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 interest that has been added to it.

Front

What is the formula for calculating the total amount with continuous compounding?

Back

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

Front

If an investment of $2,000 earns 5% interest compounded annually, what will be the amount after 10 years?

Back

Using the formula A = P(1 + r/n)^(nt), the amount will be A = 2000(1 + 0.05/1)^(1*10) = $3,252.19.