Question

Derek borrows $264,972.00 to buy a house. He has a 30-year mortgage with a rate of 4.45%. After making 139.00 payments, how much does he owe on the mortgage?

A bank offers 8.00% on savings accounts. What is the effective annual rate if interest is compounded continuously?

Please explain

Answer 1

(1)Mortgage Amount = $ 264972, Interest Rate = 4.45 %, Mortgage Tenure = 30 years or 360 months (number of monthly payments), Let the monthly payments be $ P

Monthly Interest Rate = (4.45/12) = 0.37083 %

Therefore, 264972 = P x (1/0.0037083) x [1-{1/(1.0037083)^(360)}]

P = 264972 / 198.524 ~ $ 1334.707

The amount owed post completion of 139 monthly payments should equal the total present value of the remaining monthly repayments discounted at the applicable monthly interest rate.

Therefore, Balance Mortgage = 1334.707 x (1/0.0037083) x [1-{1/(1.0037083)^(360-139)}] = $ 201087.8

(2) Annual Percentage Rate= 8 %

Let the EAR be R

Therefore, if compounding is done continuously, then [1+R] = e^(0.08 x 1) = 1.08329

R = 1.08329 - 1 = 0.08329 or 8.329 % ~ 8.33 %