Question

QUESTION 9 (10 marks) You purchase a new house for $825.000 and makea 25% down payment You arrnge mortgage for the balance with an amortization period of 25 years and an interest rate of 575 % compounded semi-annually a. Calculate the size of your monthly payment rounded up to the nearest cent. (4) b. How much interest will you pay in the fourth year your mortgage? (2) c. Find the size of your final payment (assuming no change in interest rate during the 25 years. (2) d. How much do you owe after five years? (2)

Answer 1

Here the nominal rate is 5.75% and as this is compounded semi-annually we get the following:

(1+i)^12 – 1 = (1+5.75%/2)^2 -1

Or i = (1+5.75%/2)^(1/6) – 1

= 0.473525%. This is the monthly rate. Thus the annual rate will be = 0.473525%*12 = 5.682306%

(a): Here nper = 25*12 = 300, PV = $825,000 – (25% of 825,000) = $618,750 and rate = 0.473525% (monthly). Using the “PMT” function we get: PMT(0.473525%, 300, 618750) = $3,867.32

Thus size of monthly payments will be = $3,867.32

(b): Interest paid in 4^th year can be computed by making a loan repayment table and then adding all interest payments for months 37^th to 48^th.

The amount is: $32,721.14

Month	Opening bal. of loan	Payment	Interest	Principal paid	Closing bal. of loan
37	582,051.59	3,867.32	2,756.16	1,111.16	580,940.43
38	580,940.43	3,867.32	2,750.90	1,116.42	579,824.00
39	579,824.00	3,867.32	2,745.61	1,121.71	578,702.29
40	578,702.29	3,867.32	2,740.30	1,127.02	577,575.27
41	577,575.27	3,867.32	2,734.97	1,132.36	576,442.91
42	576,442.91	3,867.32	2,729.60	1,137.72	575,305.19
43	575,305.19	3,867.32	2,724.22	1,143.11	574,162.09
44	574,162.09	3,867.32	2,718.80	1,148.52	573,013.57
45	573,013.57	3,867.32	2,713.37	1,153.96	571,859.61
46	571,859.61	3,867.32	2,707.90	1,159.42	570,700.18
47	570,700.18	3,867.32	2,702.41	1,164.91	569,535.27
48	569,535.27	3,867.32	2,696.89	1,170.43	568,364.84

(c): The total amount of final payment will be = $3,867.32. Of this $3,849.10 will go towards principal payment and $18.23 will be the interest component.

(d): The amount owed after 5 years (i.e. 60 months) = $553,879.79

Month	Opening bal. of loan	Payment	Interest	Principal paid	Closing bal. of loan
58	557,578.39	3,867.32	2,640.28	1,227.05	556,351.35
59	556,351.35	3,867.32	2,634.47	1,232.86	555,118.49
60	555,118.49	3,867.32	2,628.63	1,238.70	553,879.79