Question

A bank account yields 7 percent interest, compounded annually. If you deposit $1,000 in the account, what will the account balance be after 5 years?

Answer 1

`$1,402.55`

Explanation:

Your total money, after depositing `P` dollars in an account earning `r` interest per year for `t` years, is given by the formula:
`A=P(1+r)^t`

The problem has given us the following:

• `P`, the principal amount of the deposit (how much money you start with), is `$1,000`.
• `r`, the interest rate per year, is `7%` (which, as a decimal, is `0.07`).
• `t`, the number of years, is `5`.

Using this info, we plug into the formula and solve:
`A=P(1+r)^t`
`A=1000(1+0.07)^5`
`A=1000(1.07)^5~~$1,402.55`

Compare this to how much money you would make without compound interest:
`A=P(rt+1)`
`A=1000(0.07*5+1)`
`A=1000(1.35)=$1,350`

You would make about `$52` less, which is why it's always better to go for a compound interest account, rather than a normal interest account.