Compound Interest

Created Feb. 7, 2024 by Marissa K


Compound Interest

In a real-world context, compound interest can be explained through the example of putting money in a bank. If you put $50 in a savings account, the bank will pay you interest on all the money in the savings account, including the interest they've previously paid you. Since the total amount of money will increase exponentially over time, the formula for calculating compound interest is exponential.


Compound Interest Formula:


formula

formula


A=the amount of money in the account at any time

P=principal, or original amount in the account

r=annual interest rate

n=number of compounding periods

t=time (number of years)



Solving Compound Interest Problems

Let's look at an example of a compound interest problem.

Emma started out with $60 in her savings account. If the bank pays 6% interest, and the money is compounded annually, how much money will be in her account at the end of one year?

To solve, all we need to do is find the value for each variable, and plug the numbers into the formula.

We're trying to solve for "A," the amount in her account at a certain time.

For the principal value "P," we will plug in the original amount in her account, which is $60.

We have to plug in the interest rate, (r) as a decimal. The bank pays 6% interest, which would be .06 in decimal form.

The number of compounding periods is what we plug in for n. If the money is compounded annually, the value for n would be 1.

"t" is for time, and the problem wants us to find the total amount of money after one year, so t=1.


When we plug all of those numbers into the formula, we get:


formula2

formula2

The answer is 63.6, meaning that at the end of one year, Emma will have a total of $63.60 in her savings account.


Tips

  • Make sure the interest rate is in the correct decimal form. 80% is 0.80, and 8% is 0.08.
  • The value for "n," the number of compounding periods, won't always be one. If the problem says semiannually, n will be 2. If the problem says monthly, n will be 12, because there are 12 months in one year.



Summary

When solving compound interest problems, variables should be defined and plugged into the equation A=P(1+r/n)^nt.

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