Question

The bank has agreed to give you a mortgage for $400,000 to buy a new house. Current mortgage rates have an APR of 4% compounded semi-annually for a term of 25 years. How much interest will you pay in total over the life of the loan?

Select one:

a. $121,433.25

b. $143,645.25

c. $231,224.25

d. $237,378.25

e. None of the above.

Answer 1

Sol:

Principal (P) = $400,000

Interest rate (r) = 4% (semi annual) = 4%/2 = 2%

Period (n) = 25 (semi annual) = 25 x 2 = 50, (Monthly) = 25 x 12 = 300

Now to compute interest paid in total over the life of the loan we have to find Equal Monthly Payment (EMI):

Effective interest rate = (1+r/n)^n -1

2% = (1+r) ^6 - 1

Monthly interest rate (r) = 0.00330589

EMI = P x r (1+r)^n/(1 + r)^n – 1

EMI = 400000 x 0.00330589 (1+0.00330589)^300/(1+0.00330589)^300 - 1

EMI = 1322.356 (1.00330589)^300/(1.00300589^300)-1

EMI = 1322.356 x (2.6915877678 / 1.6915877678)

EMI = 1322.356 x 1.591160576

EMI = 2104.08

Total loan paid = EMI x Period = 2104.08 x 300 = 631224.25

Interest paid in total over the life of the loan = Total loan paid - Principal

Interest paid in total over the life of the loan = 631224.25 - 400000 = 231224.25

Therefore interest paid in total over the life of the loan will be $231,224.25

Answer is C - $231,224.25