Question

What price home can you afford if you pay a down payment of $50,000 and take out a 15 year 5% loan with a monthly mortgage payment of $1,775?

a. 224,458
b. 274,458
c. 330,650
d. 380,650

Answer 1

To solve this problem, we need to use the formula for calculating the mortgage payment which is given by:

P = [r*PV(1 + r)^n]/[(1 + r)^n - 1]

Where:

- P is the mortgage payment

- r is the monthly interest rate (annual interest rate divided by 12)

- PV is the loan amount

- n is the number of payments (loan term in months)

Here, we know the mortgage payment (P = $1,775), the monthly interest rate (r = 5% / 12 = 0.004167), and the number of payments (n = 15 * 12 = 180 months). We need to find the loan amount (PV).

Rearranging the formula to solve for PV gives:

PV = P * [(1 + r)^n - 1] / [r * (1 + r)^n]

Substituting the known values into this formula gives the loan amount:

let P = 1775;

let r = 5 / 100 / 12; // monthly interest rate

let n = 15 * 12; // loan term in months

let PV = P * ((Math.pow(1 + r, n) - 1) / (r * Math.pow(1 + r, n)));

console.log(PV); // outputs: 224,458.04

This gives the loan amount as approximately $224,458.04.

However, this is just the loan amount. The price of the home would be the loan amount plus the down payment. Since the down payment is $50,000, we add this to the loan amount to get the home price:

let downPayment = 50000;

let homePrice = PV + downPayment;

console.log(homePrice); // outputs: 274,458.04

This gives a home price of approximately $274,458.04. So, the closest answer to the options provided would be (b) $274,458.