Jamal deposited $4,000 in a savings account at a rate of 6.75%
compounded quarterly. How much was in his account after six months?
a. $4,136.14
b. $135
c. $4,135
d. $136.14
The first step is to determine the number of compounding periods in six months. Since the interest is compounded quarterly, there are 2 compounding periods in 6 months.
We can use the formula for compound interest to calculate the amount in Jamal's account after 6 months:
A = P(1 + r/n)^(nt)
where:
A = amount after 6 months
P = initial principal (deposit) = $4,000
r = annual interest rate = 6.75% = 0.0675
n = number of times interest is compounded per year = 4 (quarterly)
t = time in years = 6 months / 12 months = 0.5 years
Plugging in the values, we get:
A = 4000(1 + 0.0675/4)^(4*0.5)
A = $4,136.14
Therefore, the answer is (a) $4,136.14.