In 15 years’ time you wish to purchase a house in Avalon Park, FL currently valu
ID: 2784019 • Letter: I
Question
In 15 years’ time you wish to purchase a house in Avalon Park, FL currently valued at $180,000. The value of the asset is expected to increase at a growth rate of 2.75% per year. You wish to set aside equal end-of-monthly payments so that in 15 years’ time you would buy the house for cash. What is the equal monthly amounts to set aside, assuming that you could earn a 9% return on your set aside amounts over the period? This simulation is best handled in two parts, as we did in class, as follows:
Projected asset value:
……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………$_________
Set Aside end-of-month payments (PMT) would be:
…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………... $___________
Explanation / Answer
Projected asset value Using future value of sum , we can calculate the asset value at the end of 15th year FV = P * (1+g)^n FV = Future value i.e. projected asset value = ? P = Present Value of house = $180000 g = growth rate = 2.75% n = no.of years = 15 FV = 180000 * (1+0.0275)^15 FV = 270395.81 Projected asset value = $2,70,395.81 Set Aside end-of-month payments (PMT) would be: We can use future value of annuity to calculate the monthly amount set aside. FV of annuity = A * {[(1+r)^n - 1]/r} FV of annuity = future value of monthly set aside amount = projected asset value = $2,70,395.81 A = Annuity i.e.monthly set aside amount = ? r = rate of interest per month = 9%/12 = 0.0075 n = no.of months = 15 years * 12 = 180 270395.81 = A * {[(1+0.0075)^180 - 1]/0.0075} 270395.81 = A * 378.41 A = 714.57 Set Aside end-of-month payments (PMT) would be: $714.57