Question

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

Answer 1

No down payment = $73 267; 10 % down payment = $81 408

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.