Question

You invest $1200 and it grows at a rate of 7% for 5 years. Which expression gives the value of your investment?

Answer 1

The expression gives the value of your investment is $A=1200(1.07)^{5}$

The value of investment after 5 years is $ 1683.06

Solution:

Given that You invest $1200 and it grows at a rate of 7% for 5 years

To find:  Expression that gives the value of your investment

From given information,

Principal = $ 1200

rate of interest = 7 %

number of years = 5 years

The formula for compound interest, including principal sum, is:

$A=p\left(1+\frac{r}{n}\right)^{n t}$

Where,

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

Assuming interest is compounded annually, n = 1

$r = 7 \% = \frac{7}{100} = 0.07$

Substituting the values we get,

$A=1200\left(1+\frac{0.07}{1}\right)^{1 \times 5}$

$\begin{aligned}&A=1200\left(1+\frac{0.07}{1}\right)^{1 \times 5}\\\\&A=1200(1.07)^{5}\\\\&A=1200 \times 1.402=1683.06\end{aligned}$

Thus the value of investment after 5 years is $ 1683.06