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: Person Annuity Payment Type of Account Expected Annual Return
Mary Kate $3,900 Savings 3%
Ashley 4,900 CDs 5
Dakota 5,900 Bonds 6
Elle 5,900 Stocks 12

Required:
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?

Mary Kate: $103,528.15

Ashley: $135,377.97

Dakota: $166,294.24

Elle: $187,409.00

Explanation:

Mary Kate

First, calculate the future value of investment

Future value of Investment = Annuity payment x ( 1 + Interst rate )^numbers of years - 1 / Interst rate = $3,900 x ( 1 + 3% )^5 - 1 / 3% = $20,705.63

Amount affordable = Future value of investment / Rate of down payment = $20,705.63 / 20% = $103,528.15

Ashley

First, calculate the future value of investment

Future value of Investment = Annuity payment x ( 1 + Interst rate )^numbers of years - 1 / Interst rate = $4,900 x ( 1 + 5% )^5 - 1 / 5% = $27,075.59

Amount affordable = Future value of investment / Rate of down payment = $27,075.59 / 20% = $135,377.97

Dakota

First, calculate the future value of the investment

Future value of Investment = Annuity payment x ( 1 + Interst rate )^numbers of years - 1 / Interst rate = $5,900 x ( 1 + 6% )^5 - 1 / 6% = $33,258.85

Amount affordable = Future value of investment / Rate of down payment = $33,258.85 / 20% = $166,294.24

Elle

First, calculate the future value of the investment

Future value of Investment = Annuity payment x ( 1 + Interst rate )^numbers of years - 1 / Interst rate = $5,900 x ( 1 + 12% )^5 - 1 / 12% = $37,481.80

Amount affordable = Future value of investment / Rate of down payment = $37,481.80 / 20% = $187,409.00

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