Given:
a)
Future value: 8000
Annual interest rate: 10%
Time invested = 7 years.
Compounding frequency = annually
Recall the formula for computing future value with compound interest is
[tex]S=P(1+\frac{r}{n})^{nt}[/tex]
Here Compounding frequency is annually so n=1.
[tex]i\text{ \%=}\frac{r}{n}\text{ \%}[/tex]
Substitute r=10 and n=1, we get
[tex]i\text{ \% =10 \%}[/tex]
We get i %=10 %
Substitute S=8000, r=10/100=0.1, t=7 and n=1 in the formula, we get
[tex]8000=P(1+\frac{0.1}{1})^{1\times7}[/tex]
[tex]8000=P(1+0.1)^7[/tex]
[tex]8000=P\times1.949[/tex][tex]P=\frac{8000}{1.949}=4104.669[/tex]
The present value is $4104.67
The interest = future value - present vlaue
[tex]\text{Interest = 8000-4104.67=}3895.33[/tex]
Interest earned = $3895.33
