Question

1. You are planning to buy a new house. You currently have $35,000 and your bank told you that you would need a 15% down payment plus an additional 4% in closing costs. If the house that you want to buy costs $250,000 and you can make a 7% annual return on your Investment, determine the following: a) b) When will you have enough money for the down payment and closing costs, assuming that the $35,000 is the only investment that you make? You decide that you want to buy the house in 3 years. How much do you need to save every month to achieve ural?

Answer 1

a)

The money required for the down payment and closing costs = 0.15 x $ 250,000 + 0.04 x $ 250,000

The money required for the down payment and closing costs = $ 47,500

Using the future value of investment equation, we can calculate the time when there will be enough money for the down payment and closing costs.

Future value of investment Present value X (1+ interest rate)"

S47,500 $35,000 x (1+0.07)

$47,500 1.07" $35,000

1.07 1.357142857

Taking natural log on both sides of the equation

In 1.357142857 n In 1.07

In 1.357142857 n 1.07

n = 4.51 years

Thus in 4.51 years, there will be enough money for the down payment and closing costs.

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b)

To buy the house in 3 years, the money to be saved each month for the down payment and closing costs is calculated as follows

A (1+rn-1 Future value of annuity= r

12x3 0.07 1 + 12 -1 S47,500 0.07 12 4

The value of A is the amount to be saved each month to achieve the goal in 3 years

A = $ 1,189.58

Thus to buy the house in 3 years, a savings of $ 1,189.58 has to be made each month.