# Compound Interest

One very important exponential equation is the compound-interest formula:

\(A = P \left( 1+ \Large \frac{r}{n} \normalsize \right) ^{nt}\)

…where “A” is the ending amount, “P” is the beginning amount (or “principal”), “r” is the interest rate (expressed as a decimal), “n” is the number of compoundings a year, and “t” is the total number of years.

Let’s look at an example. Suppose Yoshi has $500 that she invests in an account that pays 3.5% interest compounded quarterly. How much money does Yoshi have at the end of 5 years?

First, identify the information given.

Yoshi has $500 that she invests, so that is her initial, or principal amount, \(P = $500\). The bank pays 3.5% interest, which is the rate. Convert that to a decimal, then \(r = 0.035\). The number of compoundings per year is quarterly, so \(n = 4\). Yoshi is going to leave the money in the bank for 5 years, so \(t = 5\).

Now, using the formula, \(A=$500 \left( 1 + \Large \frac{0.035}{4} \normalsize \right) ^{4*5}\)

Why do you suppose the interest rate is divided by the number of compounds?

Why do you suppose the number of years is multiplied by the number of compounds in the exponent position?

Justify that this is an example of an exponential growth function.

ANS: $595.17