Claude is buying a house. He expects his budget to allow a monthly payment of $1250...

Claude is buying a house. He expects his budget to allow a monthly payment of $1250 on a 25-year mortgage with an interest rate of (6.8%,2). If Claude makes a 10 percent down payment, determine the most he can pay for the house.

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Expert Solution

Annual Interest Rate = 6.80% compounded semiannually

Semiannual Interest Rate = 6.80% / 2
Semiannual Interest Rate = 3.40%

Effective Annual Rate = (1 + Semiannual Interest Rate)^2 - 1
Effective Annual Rate = (1 + 0.0340)^2 - 1
Effective Annual Rate = 1.069156 - 1
Effective Annual Rate = 0.069156 or 6.9156%

Monthly Interest Rate = (1 + Effective Annual Rate)^(1/12) - 1
Monthly Interest Rate = (1+ 0.069156)^(1/12) - 1
Monthly Interest Rate = 1.005588 - 1
Monthly Interest Rate = 0.005588 or 0.5588%

Monthly Payment = $1,250
Time Period = 25 years or 300 months

Amount Borrowed = $1,250/1.005588 + $1,250/1.005588^2 + … + $1,250/1.005588^299 + $1,250/1.005588^300
Amount Borrowed = $1,250 * (1 - (1/1.005588)^300) / 0.005588
Amount Borrowed = $1,250 * 145.325516
Amount Borrowed = $181,656.90

Amount Borrowed = 90% * Cost of House
$181,656.90 = 90% * Cost of House
Cost of House = $201,840.99

Therefore, Claude can pay a maximum sum of $201,840.99 for the house.

jeff jeffy answered 1 year ago

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