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 of money you need to invest today), r is the interest rate per period, and n is the number of periods.Given:- FV = $20,000- Annual interest rate (r) = 18.75% or 0.1875- Since the interest rate is annual and we're dealing with 9 months, we need to adjust the rate and the period to reflect this. The period (n) = 9/12 = 0.75 years.Rearranging the formula to solve for PV gives us: $PV = \frac{FV}{(1 + r)^n}$Plugging in the given values: $PV = \frac{20,000}{(1 + 0.1875)^{0.75}}$Calculating this gives us approximately $17,534, which means you would need to invest about $17,534 today to have $20,000 in 9 months at an 18.75% interest rate.

How Much Money Would One Have to Invest Today at 18.75