MATH SOLVE

4 months ago

Q:
# Scor Question Help 4.D.49 You can afford monthly payments of $500. If current mortgage rates are 2.83% for a 15-year fixed rate loan, how much can you afford to borrow? If you are required to make a 10% down payment and you have the cash on hand to do it, how expensive a home can you afford? (Hint: You will need to solve the loan payment formula for P.) How much can you afford to borrow? S(Round to the nearest dollar as needed.) orary cess esources 6ew

Accepted Solution

A:

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.