Answer:
$97.99
Step-by-step explanation:
3 months is "fraction" of a year
How much?
3/12 = 1/4th of a year
So, the interest earned in 3 months, is annual interest divided by 4.
We can use compound interest formula shown below to solve this easily:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where
A is the future amount
P is the present amount (principal)
r is the rate of interest annual
n is the number of compounding in a year
t is the time in years
So, let's find the given information:
P = 6500
r = 6% = 6/100 = 0.06
n = 12 [compounded monthly, so 12 times compounding]
t = 1/4 = 0.25 [3 months = 0.25 of a year]
Now, substituting, we find the value of 6500 after 3 months:
[tex]A=P(1+\frac{r}{n})^{nt}\\A=6500(1+\frac{0.06}{12})^{12*0.25}\\A=6500(1.005)^{3}\\A=6597.99[/tex]
So 6500 became 6597.99 in 3 months. The excess amount is the interest earned.
Interest Earned = 6597.99 - 6500 = $97.99
