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. Marti and Sue 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?

Question

Quizplus · Accepted Answer

To determine the amount that must be deposited at the end of each year, we need to use the present value (PV) formula:

PV = FV / (1 + r)^n

Where:
FV = future value (in this case, $180,000)
r = interest rate (5%)
n = number of years (4)

Using Table 9-1 to calculate the PV factor, we get:

PV factor for 1 year at 5% = 0.9524
PV factor for 2 years at 5% = 0.9070
PV factor for 3 years at 5% = 0.8638
PV factor for 4 years at 5% = 0.8227

So, to calculate the required deposit at the end of each year, we divide the future value by the PV factor for the corresponding year:

Deposit at the end of year 1 = $180,000 / 0.8227 = $218,684.95
Deposit at the end of year 2 = $180,000 / 0.8638 = $208,559.22
Deposit at the end of year 3 = $180,000 / 0.9070 = $198,537.61
Deposit at the end of year 4 = $180,000 / 0.9524 = $189,610.75

Adding up these deposits, the total amount that must be deposited over the course of 4 years is:

$218,684.95 + $208,559.22 + $198,537.61 + $189,610.75 = $815,392.53

Therefore, the closest answer choice is C) $41,763.

The Solution to This Problem Requires Time Value of Money