# Actually Applicable Application Problems and Brainteasers/Compound Interest

## Overview

Compound interest is used to calculate how a savings account or a debt will grow over time due to interest payments/charges, in the absence of other deposits, payments, fees, etc. This is a very Actually Applicable type of problem because you can use it to explore some ways of getting things you want or need.

## General Method

The formula for compound interest is A=P(1+r/n)^(nt), where those variables mean:

• I: interest
• P: Principal
• r: rate (usually APR, "annual percentage rate")
• t: time (usually in years)
• n: number of compounding periods per year

## Problems

### Forgotten Savings Account

If you deposit \$800 in a savings account at 5% with quarterly compounding, then forget to check on it until you receive a letter from that bank 10 years later, how much money will be in that account at that time?

### Goal: Amount of Interest

If you have \$200 and would like it to earn \$100 in interest (that is, grow to \$300), how long will it take to do so in a savings account at 2% with monthly compounding?

### Effective APR

What APR with annual compounding corresponds to a 3% APR with daily compounding? (Hint: it will be more than 3% because compounding makes money grow more quickly. Try plugging in a \$100 principal.)