Mary Kate, Ashley, Dakota, and Elle each want to buy a new home. Each needs to s
ID: 2463412 • Letter: M
Question
Mary Kate, Ashley, Dakota, and Elle each want to buy a new home. Each needs to save enough to make a 20% down payment. For example, To buy a $100,000 home, a person would need to save $20,000. At the end of each year for five years, the women make the following investments:
What is the maximum amount each woman can spend on a home, assuming she uses her accumulated investment account to make a 20% down payment?
Person Annuity Payment Type of Account Expacted Annual Return Mary Kate $2,200 Savings 2% Ashley $3,200 CDs 4% Dakota $4,200 Bonds 6% Elle $4,200 Stocks 12%Explanation / Answer
n = 5 years
R = expected return received for annuity payments
Future value of annuity formula will be used to solve this problem.
Case of Mary Kate
Future value of investment = annuity payment*((1+R)^n – 1)/R = 2200*((1+2%)^5 – 1)/2%
Future value of investment = $11448.89
Since, this investment value is to finance the 20% down payment on home investment.
Thus
Investment that can be afforded by Mary Kate = 11448.89 / 20% = $57244.45
Case of Ashley
Future value of investment = annuity payment*((1+R)^n – 1)/R = 3200*((1+4%)^5 – 1)/4%
Future value of investment = $17332.23
Since, this investment value is to finance the 20% down payment on home investment.
Thus,
Investment that can be afforded by Ashley = $17332.23 / 20% = $86661.15
Case of Dakota
Future value of investment = annuity payment*((1+R)^n – 1)/R = 4200*((1+6%)^5 – 1)/6%
Future value of investment = $23675.79
Since, this investment value is to finance the 20% down payment on home investment.
Thus,
Investment that can be afforded by Dakota = 23675.79 / 20% = 118379
Case of Elle
Future value of investment = annuity payment*((1+R)^n – 1)/R = 4200*((1+12%)^5 - 1)/12%
Future value of investment = $26681.96
Since, this investment value is to finance the 20% down payment on home investment.
Thus,
Investment that can be afforded by Elle = 26681.96 / 20% = $133409.8
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