Question

The Young family is purchasing a $130,000 house with a VA mortgage. The bank is offering them a 25- year mortgage with an interest rate of 9.5%. They have $20,000 invested that they could use for a down payment. Since they don’t need a down payment, Mr. Young wants to keep the money invested. Mrs. Young believes that they should make a down payment of $20,000.

Option 1 DO NOT MAKE down payment If they Young’s do not make the down payment they will finance $130,000 with monthly payments of $1135.81. The total cost of the house would be $340,473 and $210,743 of this would be interest. If they invest the $20,000 in an account with an APR of 10% compounded quarterly, in 25 years the accumulated amount of the investment would be $236,274.33.

1) If the Young’s choose option 1 and do not make the down payment, what is the difference between the amount they have in their investment after 25 years and the total cost that they spend on the house?

Option 2 MAKE a $20,000 down payment

2) Determine the amount of the mortgage if they make the $20,000 down payment.

3) Determine the monthly payment for principal and interest if they make a $20,000 down payment.

4) Determine the total cost of the house if they make a down payment of $20,000.

5) How much of the total cost is interest?

6) If the Youngs use the $20,000 as a down payment, their monthly payment will decrease. Determine the difference of the monthly payments from option 1 to option 2.

7) Assume that the difference in monthly payments is invested in an ordinary annuity each month at a rate of 6% compounded monthly for 25 years. Determine the value of the investment in 25 years.

8) If the Young’s choose option 2 and make the down payment, what is the difference between the amount they have in their ordinary annuity after 25 years and the total cost that they spend on the house?

9) Use the information from options 1 and 2 to analyze the problem. Would you recommend that the Youngs not make the down payment and keep the $20,000 invested (as in option 1) or make the down payment of $20,000 and invest the difference in their monthly payments (as in option 2)? Explain.

Answer 1

	Option 1
1-	What is the difference between the amount they have in their investment and the total cost they spend on the house	total cost spend on house-value of investment	340473-236274.33	104198.67
	Option 2
2-	Amount of mortgage if down payment is made	cost of house-down payment	130000-20000	110000
3-	Amount of monthly payment	amount mortgaged/PVAF at .79166% for 300 months	110000/114.4548	961.08
	PVAF at .79166% for 300 months	1-(1+r)^-n /r	1-(1.007916)^-300 /.79166%	.906093/.79166%	114.4548
4-	total cost of the house	down payment+(monthly payment*no. of months)	20000+(961.08*300)	308324
5-	total cost is interest	total cost of the house-down payment-amount mortgaged	308324-20000-110000	178324
6-	Difference in monthly payment	monthly payment in option1-montly payment in option 2	1135.81-961.08	174.73
7-	value of investment after 25 years or 300 months	difference in monthly payment*FVAF at .5% for 300 months	174.73*692.992	121086.49
	FVAF at .5% for 300 months	(1+r)^n -1/ r	(1.005)^300 -1 /.5%	3.46496/.5%	692.992
8-	difference in ordinary annuity and total cost of house	total cost of house-value of annuity investment	308324-121086.49	187237.51
9-	option 1 would be better as the difference between cost of house and value of annuity investment is low