Question

11) A lender requires that monthly mortgage payments be no more than 35% of gross monthly income, with a maximum term of 30 years. Ifyou can make only a 15% down payment, what is the minimum monthly income you would need in order to purchase a $500,000 home when the interest rate is 3% APR compounded monthly? a) $1,795 b) $2,400 c) $5,120 d) $9,590

Answer 1

Cost of House = 500000

Down payment will be 15%

Down payment Amount = 500000 * 15% = 75000

Mortgage Amount = 500000 - 75000 = 425000

Interest Rate = 3% per year compounded monthly

So Effective monthly interest rate will be calculated with below mentioned formula-

i = (1+(Annual Interest Rate/Number of interest period in a year))-1 (we will ignore power factor as number of year will be 1)

i = 1+(0.03/12) - 1 = 1.0025 - 1 = 0.25%

Now we will find the average monthly payment with the help of below mentioned formula -

A = P [{i*(1+i)^N}/{(1+i)^N-1}]

P = 425000

i = 0.25%

N = 30*12 = 360

So,

A = 425000[{0.0025*(1.0025)^360}/{(1.0025)^360-1}]

A = 425000*(0.006142/1.456842)

A = 1791.817 = 1792 per month

Now, Monthly payment can not be greater that 35% of gross monthly income.

Gross Monthly Income = 1792/0.35 = 5120

Hence correct answer will be C