To solve this problem, we will use the formula for compound interest:
[tex]A_N=A_0\cdot(1+\frac{r}{k})^{N\cdot k}.[/tex]Where:
• A_N = is the amount of money after N years,
,• A_0 = is the initial amount of money,
,• r = is the interest in decimals,
,• k = is the number of compound periods per year.
In this problem, we have:
• A_0 = $850,
,• r = 7.5% = 0.075,
,• k = 1 (because the interest is simple),
,• N = 1 (after 1 year).
Replacing the data of the problem in the equation above, we get:
[tex]A_1=850\cdot(1+\frac{0.075}{1})^{1\cdot1}=850\cdot1.075=913.75.[/tex]Answer
The value of the investment after one year will be $913.75.
