Question

You are 20 years old and plan to purchase a house when you are 35

.a. The current price of the house you want to purchase is $275,000 and the price is expected to increase by 3% per year. How much will the house cost when you are 35?

b. When you are 35, the bank will require a cash down-payment of 10% of the house price to obtain a mortgage. How much will you need to save each year between age 20 and 35 to have enough for the down-payment, if you can earn 5% on your deposits? Assume end-of-year deposits.

c. Given the same data in part b., how much will you need to deposit each year to have enough for the down-payment if you make beginning-of-year deposits?

d. Suppose your parents promise to pay the down-payment when you turn 35. How much will they need to deposit today in an account that will earn 8% for the next 15 years (when you will need to the down-payment)?

Answer 1

Solution a
	Price of house	$                 275,000
	Annual inflation	3%
	Price of house after 15 years=	275000*(1+3%)^15
	Price of house after 15 years=	$           428,441.04
Solution b
	Down payment	10%
	Down payment	$             42,844.10	428441.04*10%
	FV of annuity
	P = PMT x ((((1 + r) ^ n) - 1) / r)
	Where:
	P = the future value of an annuity stream	$             42,844.10
	PMT = the dollar amount of each annuity payment	PMT
	r = the effective interest rate (also known as the discount rate)	5%
	n = the number of periods in which payments will be made	15
	FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / r)
	42844.10=	PMT x ((((1 + 5%) ^15) - 1) / 5%)
	Annual year end paymen to accumulate the down payment=	42844.10/ ((((1 + 5%) ^15) - 1) / 5%)
	Annual year end paymen to accumulate the down payment=	$               1,985.49
Solution c
	Down payment	10%
	Down payment	$             42,844.10	428441.04*10%
	FV of annuity due
	P = PMT x ((((1 + r) ^ n) - 1) / r)*(1+r)
	Where:
	P = the future value of an annuity stream	$             42,844.10
	PMT = the dollar amount of each annuity payment	PMT
	r = the effective interest rate (also known as the discount rate)	5%
	n = the number of periods in which payments will be made	15
	FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / r)*(1+r)
	42844.10=	PMT x ((((1 + 5%) ^ 15) - 1) / 5%)*(1+5%)
	Annual year begin payment to accumulate the down payment=	42844.10/ (((((1 + 5%) ^ 15) - 1) / 5%)*(1+5%))
	Annual year begin payment to accumulate the down payment=	$               1,890.95
Solution d
	Amount to be deposted today for down payment=	Down payment/(1+Interest)^period
	Amount to be deposted today for down payment=	42844.10/(1+5%)^15
	Amount to be deposted today for down payment=	$             20,608.74