Question

If money can be invested at 3.6% compounded quarterly, which is larger, $2314 now or $3000 in 8 years? Use present value to decide. The present value of $3000 in 8 years is $ (Do not round until the final answer. Then round to the nearest cent as needed.)

Answer 1

$3000 in 8 years is larger than $2314 now.

Step-by-step explanation:

To determine which is larger, $2314 now or $3000 in 8 years, we can use present value to compare them. The present value of $3000 in 8 years is:

PV = FV / (1 + r/n)^(n*t)

Where PV is the present value, FV is the future value, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, the interest rate is 3.6%, and the compounding is done quarterly:

PV = 3000 / (1 + 0.036/4)^(4*8) = $2407.58

Therefore, $2407.58 is the present value of $3000 in 8 years. Since $2314 is less than $2407.58, $3000 in 8 years is larger.