Respuesta :
The expression gives the value of your investment is [tex]A=1200(1.07)^{5}[/tex]
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:
[tex]A=p\left(1+\frac{r}{n}\right)^{n t}[/tex]
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
[tex]r = 7 \% = \frac{7}{100} = 0.07[/tex]
Substituting the values we get,
[tex]A=1200\left(1+\frac{0.07}{1}\right)^{1 \times 5}[/tex]
[tex]\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}[/tex]
Thus the value of investment after 5 years is $ 1683.06
