Olga deposited $1,500 in a savings account that pays 7.5% interest,
compounded quarterly. What is the balance in her account at the
beginning of the fourth quarter?
a. $1,590
b. $1,560
c. $1,585.97
d. $1,591.81
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = Final balance
P = Principal (initial amount deposited)
r = Annual interest rate as a decimal
n = Number of times interest is compounded per year
t = Time in years
In this problem:
P = $1,500
r = 7.5% = 0.075 (note that it's given as an annual rate, so we need to convert to a decimal)
n = 4 (quarterly compounding means 4 times per year)
t = 3/4 (since we're looking for the balance at the beginning of the fourth quarter, which is 3/4 of a year)
Substituting these values into the formula gives:
A = $1,500(1 + 0.075/4)^(4*3/4)
A = $1,585.97 (rounded to the nearest cent)
Therefore, the answer is (c) $1,585.97.