We have been given that Nicolas has $6,500 to deposit into an account which earns 3.25% interest compounded annually. We are asked to find amount of interest earned at the end on 8 years.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
[tex]3.25\%=\frac{3.25}{100}=0.0325[/tex]
[tex]A=6500(1+\frac{0.0325}{1})^{1\cdot 8}[/tex]
[tex]A=6500(1+0.0325)^{8}[/tex]
[tex]A=6500(1.0325)^{8}[/tex]
[tex]A=6500(1.2915775352963673)[/tex]
[tex]A=8395.253979[/tex]
Now we will subtract principal amount from final amount to find amount of interest as:
[tex]\text{interest}=8395.253979-6500[/tex]
[tex]\text{interest}=1895.253979\approx 1895.25[/tex]
Therefore, Nicolas would have earned $1895.25 in interest at the end of 8 years.
