# Actually Applicable Application Problems and Brainteasers/Compound Interest

## Overview[edit]

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[edit]

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[edit]

### Forgotten Savings Account[edit]

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[edit]

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[edit]

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.)

### Make Your Own Problem[edit]

Open a savings account and ask what the account's APR and compounding frequency are. Deposit some money in it and calculate how much money will be in the account in 5 years if you don't add any more money to it.

Pick something you would like to buy and find out how long it would take to buy it with whatever you can deposit into a savings account now and that savings account's compounding period and interest rate.