Kurt wants to have $25,000 in an investment account 4 years from now. The account will pay 0.2 percent interest per month. If he saves money every month, starting one month from now, how much will he have to save each month to reach his goal?

Question

Quizplus · Accepted Answer

The correct answer is A.The formula for calculating the future value of an investment is:FV = PV * (1 + r)^ntwhere:FV is the future valuePV is the present valuer is the monthly interest raten is the number of times per year that interest is compoundedt is the number of yearsIn this case, we have:FV = $25,000PV = ?r = 0.2% = 0.002n = 12 (since interest is compounded monthly)t = 4Substituting these values into the formula, we get:$25,000 = PV * (1 + 0.002)^12*4$25,000 = PV * (1.002)^48$25,000 = PV * 1.0968Dividing both sides by 1.0968, we get:PV = $22,800.65This means that Kurt needs to save $22,800.65 in the investment account today in order to have $25,000 in 4 years.To calculate how much he needs to save each month, we can use the formula:PMT = PV * (r / (1 - (1 + r)^-nt))where:PMT is the monthly paymentPV is the present valuer is the monthly interest raten is the number of times per year that interest is compoundedt is the number of yearsSubstituting the values we know into the formula, we get:PMT = $22,800.65 * (0.002 / (1 - (1 + 0.002)^-12*4))PMT = $22,800.65 * (0.002 / (1 - (1.002)^-48))PMT = $22,800.65 * (0.002 / (1 - 0.9048))PMT = $22,800.65 * (0.002 / 0.0952)PMT = $22,800.65 * 0.021PMT = $496.75Therefore, Kurt needs to save $496.75 each month to reach his goal of having $25,000 in the investment account in 4 years.

Kurt Wants to Have $25,000 in an Investment Account 4