Answer:
[tex]\$180.55[/tex]
Step-by-step explanation:
step 1
Simple interest
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=10\ years\\ P=\$2,250\\r=4\%=4/100=0.04[/tex]
substitute in the formula above
[tex]A=2,250(1+0.04*10)[/tex]
[tex]A=2,250(1.4)[/tex]
[tex]A=\$3,150[/tex]
step 2
Interest compounded annually
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$2,250\\r=4\%=4/100=0.04\\n=1[/tex]
substitute in the formula above
[tex]A=2,250(1+\frac{0.04}{1})^{1*10}[/tex]
[tex]A=2,250(1.04)^{10}[/tex]
[tex]A=\$3,330.55[/tex]
step 3
Find the differences between the two final amounts
[tex]A=\$3,330.55-\$3,150=\$180.55[/tex]
