Question

How long will it take for the balance of an account to double if the savings account earns 0.75% annual interest compounded monthly?

Hint: Set up the problem using the formula: A=P(1+r/n )^nt.

Answer 1

You're looking for the time
`t` that it takes for the principal
`P` to double, so
`A=2P`. Dividing both sides of the formula by
`P` leaves you with


`2=\left(1+\frac rn\right)^(nt)`

You're given that the account earns 0.75% interest and that the interest is compounded monthly, so
`r=0.0075` and
`n=12`.


`2=\left(1+(0.0075)/(12)\right)^(12t)`

`\ln2=\ln\left(1+(0.0075)/(12)\right)^(12t)`

`\ln2=12t\ln\left(1+(0.0075)/(12)\right)`

`t=(\ln2)/(12\ln\left(1+(0.0075)/(12)\right))\approx92.45`