# How do you calculate the percentage increase in value per year of something $350 to$800 in 7 years?

May 8, 2018

12.54% per year.

#### Explanation:

We could use the formula for compound interest.

$F V = P V {\left(1 + \frac{r}{n}\right)}^{n t}$

Where:

FV = future value.

PV = present value.

$r =$ interest rate given as a decimal.

$n =$ number of compounds per year.

$t =$ number of years.

We have:

$P V = 350$

$F V = 800$

We will assume that this is compounded annually.

$350 {\left(1 + \frac{r}{1}\right)}^{7} = 800$

${\left(1 + \frac{r}{1}\right)}^{7} = \frac{800}{350} = \frac{16}{7}$

$r = \sqrt[7]{\frac{16}{7}} - 1 \approx 0.125353197$

This is in decimal form, so.

12.54% per year. 2 d.p.