Solve the problem.
-An initial investment of $12,000 is invested for 2 years in an account that earns 4% interest, compounded quarterly. Find the amount of money in the account at the end of the period.
A) $12,865.62
B) $12,994.28
C) $994.28
D) $12,979.20

Question

Quizplus · Accepted Answer

Using the formula for compound interest:

A = P(1 + r/n)^(n*t)

where:

A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)

Plugging in the given values:

A = 12,000(1 + 0.04/4)^(4*2)
A = 12,994.28

Therefore, the amount of money in the account at the end of the period is $12,994.28, which corresponds to choice B. First, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount in the account at the end of the period, P is the initial investment, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we have:

P = $12,000
r = 0.04 (4% expressed as a decimal)
n = 4 (because interest is compounded quarterly)
t = 2

Plugging in these values, we get:

A = $12,000(1 + 0.04/4)^(4*2)
A = $12,994.28 (rounded to the nearest cent)

Therefore, the best choice is B, $12,994.28.

Solve the Problem. -An Initial Investment of $12,000 Is Invested for 2 Years