Clem deposited $5,000 in a savings account which pays 6.50/o
interest, compounded quarterly. What was his balance at the
beginning of the third quarter?
a. $5,081.25
b. $5,163.82
c. $5,247.73
d. $5,325
To solve this problem, we need to use the compound interest formula:
A = P (1 + r/n)^(nt)
where:
- A is the final amount (what we want to find)
- P is the initial principal (in this case, $5,000)
- r is the annual interest rate (6.50%)
- n is the number of times the interest is compounded per year (4, since it's compounded quarterly)
- t is the time in years (we want to find the balance at the beginning of the third quarter, or 6 months, so t = 0.5)
Plugging in these values, we get:
A = 5000 (1 + 0.065/4)^(4*0.5)
A = $5,163.82
Therefore, the answer is b. $5,163.82.