Answer:
d. $1,287.78
Explanation:
The formula for the compound interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A = final amount
P = principle (inital) amount
r = interest rate / 100
n = number of times interest is applied per time period
t = time.
Now in our case
P = 1250
r = 6/ 100 = 0.06
n = 4 (quarterly)
t = 2 quarters = 0.5 of a year
therefore, we have
[tex]A=1250(1+\frac{0.06}{4})^{4\cdot0.5}[/tex]which simplifies to give
[tex]\boxed{A=1287.78}[/tex]Hence, at the end of the second quarter, Theo's balance would be 1287.78, and therefore, choice D is the correct answer.
