Menu

Home | Resume | Blog
Videos

Compound Interest, Interest Earned

Table of Contents

• Compound Interest, Interest Earned
  • Table of Contents
  • Example 1 - Compound Interest Earned
  • Example 2 - Compound Interest Earned

The compound interest formula, shown below, only calculates the total amount with interest.

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

where:

• A is the total amount
• P is the principal, the initial amount
• r is the interest rate divided by 100
• n is the number of times the interest is compounded per year.
• t is the number of years the principal is gaining interest

To just find the interest we need to subtract the principal, the initial amount, from the formula. The formal for interest earned through compound interest becomes:

$$I = P(1 + \frac{r}{n})^{n \times t} - P$$

where I is the interest earned.

Example 1 - Compound Interest Earned

• Ashley McAshington of Asheville, N.C. invests $4,560 in Ashbank, which offers 1.8% interest compounded monthly. How much interest does she earn after 2 years.

To answer this question, we'll first identify P, r, n, and t:

• P = $4560
• r = ^1.8/₁₀₀
• n = 12
• t = 2

We can then use our new formula for interest to solve this problem:

$$I = 4560(1 + \frac{(\frac{1.8}{100})}{12})^{12 \times 2} - 4560$$

We can put this into Desmos to figure this out:

So our solution, our interest earned, is $167.

Example 2 - Compound Interest Earned

Let's look at another example:

• Timmmy McTimTim, the third, of T-town, Tennessee invests $12,000 in T-bank. T-bank offers 2.05% interest compounded daily. He leaves his money in T-bank for 15 years without withdrawing any. How much interest has Timmy McTimTim earned after 15 years?

First, let's identify P, r, n, and t:

• P = $12,000
• r = ^2.05/₁₀₀
• n = 365
• t = 15

We can now use the interst formula to find Timmmy's interest earned:

$$I = 12000(1 + \frac{(\frac{2.05}{100})}{365})^{365 \times 15} - 12000$$

Plugging this into Desmos we get:

So the interest Timmy McTimTim earned is $4,320.11 when rounded to the nearest penny.