Answer:
No down payment = $73 267; 10 % down payment = $81 408
Step-by-step explanation:
1. With no down payment
The formula for a maximum affordable loan (A) is
A = (P/i)[1 − (1 + i)^-N]
where
P = the amount of each equal payment
i = the interest rate per period
N = the total number of payments
Data:
P = 500
APR = 2.83 % = 0.0283
t = 15 yr
Calculations:
You are making monthly payments, so
i = 0.0283/12 = 0.002 358 333
The term of the loan is 15 yr, so
N = 15 × 12 = 180
A = (500/0.002 3583)[1 − (1 + 0.002 3583)^-180]
= 212 014(1 - 1.002 3583^-180)
= 212 014(1 - 0.654 424)
= 212 014 × 0.345 576
= 73 267
You can afford to spend $73 267 on a home.
2. With a 10 % down payment
Without down payment, loan = 73 267
With 10 % down payment, you pay 0.90 × new loan
0.90 × new loan = 73 267
New loan = 73267/0.90 = 81 408
With a 10 % down payment, you can afford to borrow $81 408 .
Here’s how it works:
Purchase price = $81 408
Less 10 % down = -8 141
Loan = $73 267
And that's just what you can afford.
