How much money would one have to invest today at 18.75% in order to have a total of $20,000 in 9 months?
A) $16,250
B) $23,750
C) $22,813
D) $17,534
E) $19,122

Question

Quizplus · Accepted Answer

To find out how much money one would need to invest today to have a total of $20,000 in 9 months at an interest rate of 18.75%, we can use the formula for the future value of a single sum: $FV = PV(1 + r)^n$, where FV is the future value, PV is the present value (the amount we need to find), r is the interest rate per period, and n is the number of periods. Given that the interest rate is annual, we need to adjust it for the 9-month period, which is $\frac{9}{12}$ of a year. Thus, $r = \frac{18.75\%}{12} \times 9 = 14.0625\%$. Rearranging the formula to solve for PV gives us $PV = \frac{FV}{(1 + r)^n}$. Plugging in the values, $PV = \frac{20,000}{(1 + 0.140625)^1} = \frac{20,000}{1.140625} \approx 17,534$. Therefore, one would need to invest approximately $17,534 today.

How Much Money Would One Have to Invest Today at 18.75