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Compound Interest

Table of Contents

• Compound Interest
  • Table of Contents
  • Example 1 - Compound Interest
    • Example 1 - Solution
  • Example 2 - Compound Interest
    • Example 2 - Compound Interest

The formula for compound interest is:

$$A = P(1 + \frac{r}{n})^{nt}$$

Where:

• A = the total amount
• P = the principal
• r = the interest rate divided by 100
• n = the number of times the interest is compounded per year
• t = the number of years the principal earns interest

Example 1 - Compound Interest

Allie Allister of Alstown, PA invests $6000 in Allsbank. Allsbank offers an interest rate of 2.1% compouded quarterly. Allie leaves her money in Allsbank for 10 years without withdrawing any money. How much money does Allie have in Allsbank after 10 years?

Example 1 - Solution

To figure this out we first need to identify P, r, n, and t. They are:

• P = $6000
• r = ^2.1/₁₀₀
• n = 4
• t = 10

We can then put them into our compound interest formula to find A, the total amount Allie has after 10 years:

$$A = 6000(1 + \frac{\frac{2.1}{100}}{4})^{4 \times 10}$$

Plugging this into Desmos we get:

We can round to the nearest penny to get:

• $7,398.00

Example 2 - Compound Interest

Billy McBillerson of the Billington, PA invests $2300 into Bilsbank, which offers 4.5% interest compounded semi-annually. If Billy doesn't withdraw any money, how much total money does Billy have in Bilsbank after 5 years?

Example 2 - Compound Interest

To solve this we need to identify P, n, r, and t, they are:

• P = $2300
• n = 2
• r = ^4.5/₁₀₀
• t = 5

We can then write our equation for our total amount, A, as:

$$A = 2300(1 + \frac{(\frac{4.5}{100})}{2})^{2 \times 5}$$

We'll then put this into Desmos to get our solution:

We can round our solution to:

• $2,873.17