A = P(1 + r)^t

where r is the annual interest rate and t is the number of years. Sometimes interest is compounded more often than annually, For example, if 6% interest is compounded four time per year (quarterly), then one receives 1.5% interest every three months. The more general formula for the future value of a deposit with compound intrest is:

A = P(1 + r/m)^(mt)

where m is the number of times the interest is compounded each year.

How much will $300 be worth in 2.5 years if the interest rate is 3% compounded quarterly? A = $300×(1 + .03/4)^(4×2.5) = $323.27.

It is more difficult to solve for the interest rate that will produce a given increase than in the case of simple interst. It is also more difficult to solve for the time required for a given increase, although this may be easily attained by trial and error.

Exercise: How much will $250 dollars be worth in 5 years at 6% interest compounded monthly? How long will be required for $250 to double to $500?

P = A/((1 + r/m)^mt)

to get the present value, or how much you need to put in the bank now to have a specified amount in the future. For example, if you want to give $200,000 to your nephew in 21 years, how much must you deposit in the bank now at 5% compounded quarterly? P = $200,000/((1 + .05/4)^(4×21)) = $70,444.54.

**Competency**How much money will one have in 7 years if he deposits $2000 in
the bank at 8% interest compounded monthly?

How much money must one deposit in the bank at 8% interest compounded monthly in
order to have $2000 seven years from now?

What is the effective annual yield of 8% interest compounded monthly?

**Reflection: **

**Challenge: **

April 2004