Steve MacIntosh would like to have $20,000 in 5 years time to start his own business.The amount that MacIntosh would have to invest today,assuming an interest rate of 8% compounded quarterly,in order to reach his goal is:
A)$13,612.00
B)$29,386.00
C)$79,854.00
D)$13,459.43

Question

Quizplus · Accepted Answer

To find the present value that needs to be invested, we use the formula for the present value of a future sum: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value, FV is the future value, r is the interest rate per period, and n is the total number of periods. Given an 8% annual interest rate compounded quarterly, the quarterly rate is 2% or 0.02 when expressed as a decimal. Over 5 years, there are 20 quarters (5 years * 4 quarters/year). Plugging into the formula: $PV = \frac{20,000}{(1 + 0.02)^{20}}$, which calculates to approximately $13,459.43.

Steve MacIntosh Would Like to Have $20,000 in 5 Years