Question

I put $500 in the bank. I now have $5000in the bank. Every year my money increased by 5%. How long that it takes?

Answer 1

It takes 47.19 years

Explanation:

Your amount on the bank is given by the following equation:

`P(t) = P(0)(1+r)^(t)`

In which P(t) is your current amount, P(0) is the initial amount, r is the rate it changes, and t is the time since the money has been put on the bank.

I put $500 in the bank.

This means that
`P(0) = 500`

I now have $5000 in the bank.

This means that
`P(t) = 5000`

Every year my money increased by 5%

This means that
`r = 0.05`

How long that it takes?

This is t.

`P(t) = P(0)(1+r)^(t)`

`5000 = 500(1.05)^(t)`

`(1.05)^(t) = (5000)/(500)`

`(1.05)^(t) = 10`

`\log{(1.05)^(t)} = \log{10}`

We use the following logarithms property:

`\log{a^(t)} = t\log{a}`

So

`t\log{1.05} = \log{10}`

`t = \frac{\log{10}}{\log{1.05}}`

`t = 47.19`

It takes 47.19 years