Question

Your work for a bank that requires 30-year mortgages to have an EAR of 6.676%. The mortgages have monthly payments (and monthly compounding).

(a) What is the APR of these mortgages?

(b) A customer closes a deal to purchase a $800,000 home with 20% down. Her first payment is one month from now. Ignoring taxes and insurance, what are her monthly mortgage payments be?

Answer 1

Solution:

EAR = 6.676%

Part A )

EAR = (1+ APR / 12)^12 - 1

6.676%+ 1 = (1+ APR / 12)^12

(1+ APR / 12)^12 = 1.06676

1+ APR/12 = 1.06676^(1/12) = 1.0054

APR/12 = 0.0054

APR = 12 * 0.054= 6.48%

Part B )

Loan amount = 800,000 , Down payment = 20%

Effective loan = Loan amount - down payment = 800000 - 800000* 20% = 640,000

Period = 30 years = 30 *12 = 360 , Interest rate = 6.48% /12 = 0.54%

Using PMT function in EXCEL we can find the EMI =PMT(0.54%,360, -640000)? = $4036.82

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