The solution to this problem requires time value of money calculations.Reference to Tables 9-1 through 9-4 in the text is necessary to complete the calculations. Josh and Sara want to buy a house in 4 years.If the house will cost $180,000, how much must they deposit at the end of every year for the next 4 years at 5% compounded annually in order to buy the house?
A) $32,040
B) $36,990
C) $41,763
D) $45,000

Question

Quizplus · Accepted Answer

Using Table 9-1 in the text, we can determine that the future value of $1 at 5% compounded annually for 4 years is $1.22. Therefore, the future value of $180,000 in 4 years is:

$180,000 x 1.22 = $219,600

Then, using Table 9-2 in the text, we can determine the present value of an annuity of $1 for 4 years at 5% compounded annually is 3.545. Therefore, the amount Josh and Sara need to deposit each year is:

$219,600 ÷ 3.545 = $61,979.21

To find the amount they need to deposit at the end of every year, we use Table 9-3 in the text, which shows the present value of an annuity due of $1 for 4 years at 5% compounded annually is 3.717. Therefore, the amount they need to deposit at the end of every year is:

$61,979.21 ÷ 3.717 = $16,740.74

So, the best choice is C, $41,763, which is the total amount Josh and Sara need to deposit over the 4 years ($16,740.74 x 4 = $67,962.96) minus the initial deposit they make this year ($26,199.96).

The Solution to This Problem Requires Time Value of Money