# If you invest $1500 at a rate of 7% per year, how many years will it take to earn at least$1050 in interest?

Apr 24, 2018

$8$

#### Explanation:

The formula is compound interest rate:
$P {\left(1 + \frac{r}{n}\right)}^{n \cdot t} = A$
$P$ is Principal amount;
$r$ is interest rate;
$n$ is number of compounds per year/months and etc.
$t$ is time in years/months and etc.
$A$ is last Amount

So
$1500 \cdot {\left(1 + \frac{0.07}{365}\right)}^{365 \cdot t} = \left(1500 + 1050\right)$

$1500 \cdot {\left(1 + \frac{0.07}{365}\right)}^{365 \cdot t} = 2550$

It is hard to calculate. That is why you can apply for Google. There is the compound interest rate calculator on the web.

As a result, the answer or $t$ is $8$
It means that you have to wait for $8$ years in order to earn at least extra \$1050.