Question

You are currently seeking to finance your first house. The price is $400,000. You can make a down payment of $40,000, but you must obtain a mortgage (loan) for the other $360,000. Thanks to a special first time homebuyer’s program, your bank is willing to give you a 30-year, 4.8% APR loan for the amount. Interest on the loan will be compounded monthly.

a) Calculate your monthly payment on the mortgage, assuming that the payments begin one month from the day you purchase the house.

b) You estimate that the largest payments you can afford are $1,250 per month. Calculate the maximum loan you can afford if you are only able to pay $1,250 per month given the information above.

Answer 1

a)

Loan amount (Present value of annuity) = 360000

Rate (r) = 4.8% per year or 0.4% per month (i.e. 4.8/12) or 0.004 per month

No. of payment (n) = 360 months (i.e. 30*12)

Monthly payment (P)= ??

As we know,

Present value of annuity = P * [1-(1+r)^-n]/r                       Where (1+r)^-n = 1/(1+r)ⁿ

360000 = P * [1-(1+0.004)^-360]/0.004

360000 = P * [1-0.23761]/0.004

360000 = P * 0.76239/0.004

P = (360000 * 0.004)/0.76239

P = 1888.797

P = 1888.80 (Approximately)

So, Monthly payment will be $1,888.80.

b)

If P = $1,250 per month then maximum affordable loan amount will be as followed

Present value of annuity = 1250*0.76239/0.004   (where, 0.76239/0.004 is already calculated above)

Present value of annuity   = $ 238,247

So, maximum affordable loan amount will be $ 238,247.