Question

Lara is repaying a loan of $500000 with semi-annual payments. This loan has a guaranteed interest period for 5 years in which the interest rate is given as j2= 6%. After that the interest rate changes to j4= 8%. After paying a down payment of $50000, each payment she pays for the first 5 years is $10000. After that, she pays X each time for another 10 years to totally cover this loan.

(a) Calculate X

(b) Calculate all the interest earned in year 3 and year 4

(c) Calculate all the principal covered in year 8, 9, and 10.

(d) Assume that after the 20th payment, Lara misses the next 5 payments. What is the balance of this loan after she misses those 5 payments? (i.e. what is the balance at the time when she should pay the 25th payment?)

Answer 1

It is assumed that after downpayment of $50,000 the net mortgage amount is $450,000.

Loan amount after 5 years of payments of $10,000 per half year= $490,123.58 as per the relevant portion of amortization given below.

J4=8% is equal to J2=8.08% as follows:

Part (a): Value of X (half yearly payments after 5 years)= $ 36,192.00 as follows:

Part (b):

Interest for year 3 (HYs 5 and 6)= 13939.28 + 14057.46 = $ 27,996.74

Interest for Year 4 (HYs 7 and 8)= 14179.18 + 14304.56 = $ 28,483.74

Details as per amortization schedule above.

Part (c):

Principal covered in year 8 (HYs 15 and 16)= 19204.68 + 19980.55 = $39,185.23

Principal covered in year 9 (HYs 17 and 18)= 20787.77 + 21627.59 = $42,415.36

Principal covered in year 10 (HYs 19 and 20)= 22501.35 + 23410.40 = $45,911.75

Relevant portion of amortization schedule below:

Part (d): Balance after missing 21st to 25th payments= $357,123.82

Details as follows: