Zach deposited $4,000 into an account that earns 6% annual interest compounded quarterly. He did not make any deposits or withdrawals. How much money was in the account after 5 years?

Question

A. $538.74

B $120,000

C $1,200.00

D $5,387.42

Answer 1

The formula for compound interest is given by:

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

Where:
A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = annual interest rate (as a decimal)

n = number of times that interest is compounded per year

t = number of years the money is invested or borrowed for

In this case, Zach deposited $4,000 (P) into an account that earns 6% (r = 0.06) annual interest compounded quarterly (n = 4). The money was invested for 5 years (t = 5).

Plugging the values into the formula, we have:

A = 4000(1 + 0.06/4)^(4*5)

Calculating the values inside the parentheses first:

1 + 0.06/4 = 1.015

Now, calculate the exponent:

4*5 = 20

Plugging the values into the formula:

A = 4000(1.015)^20

Using a calculator to calculate (1.015)^20:

A ≈ 4,871.70

Therefore, after 5 years, there will be approximately $4,871.70 in the account.

The closest answer choice to this result is D. $5,387.42.