Answer:
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.