Answer:
He earns $50.41 of interest.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for(in years).
In this problem, we have that:
[tex]P = 1000, r = 0.1, t = \frac{6}{12} = 0.5[/tex]
Compounded quartely
So 12/4 = 3 times a year, so [tex]n = 3[/tex]
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A = 1000(1 + \frac{0.1}{3})^{3*0.5} = 1050.41[/tex]
How much interest he earns?
A - P = 1050.41 - 1000 = 50.41
He earns $50.41 of interest.
