A couple negotiated with a vendor and purchased a two-bedroom house

Question

financed through a bank. They signed a mortgage contract for a $360,000 loan to be
repaid on a monthly basis over a 25-year term at j12 = 5% p.a. To qualify for this loan
amount, the bank required the couple to pay a compulsory 20% down payment of the
sale price of the house. The loan contract states that the interest rate will remain fixed
for the first five years, and then the interest rate will be increased by 5% every 5 years
to account for average inflation rate. At the time the couple secured the deal and
signed the loan contract, their economy was severely hit by the COVID-19 pandemic
and their employment was affected. Unfortunately, the couple received a reduction in
their income which significantly affected their ability to start the repayment as initially
planned and calculated. After negotiating with their bank, the bank allowed them to
miss the first 12 months of the repayments and permitted them to move into their new
home. The bank agreed to re-adjust their repayments to account for the missed
payment and to begin repayment from year 2 onwards, however without any
extension to the loan term. The couple are optimistic that after 12 months they will be
able to commence the repayments of the adjusted amounts. They are equally
optimistic of the future given their retirement plans and savings. According to their
assessment, they expect to double the repayment amount, whatever that maybe, in
the final 5 years of their loan term. Their bank very much looks forward to this and
has assured the couple that it will not impose any penalty for early repayments.
From the above case, calculate the following:
(a) The sale price of the house, and the down payment the couple made to qualify
for the loan in the first place. (8 marks)
(b) The monthly payment applicable in the first 5-year period, accounting for the
first 12 months of missed payments. [12 marks]
(c) The new monthly payments that will be applicable in each 5-year period over
the term of the loan. That is, the repayment required at the beginning of the 5
th
year, the 10th year, the 15th year and the 20th year [20 marks]
(d) If the couple doubles their repayment as planned, compute
i. the number of full payments they will make in the final 5 years of the loan
term [7 marks],
ii. the partial payment necessary to conclude the loan repayments, (i.e. the amount paid a month after the final full payment [7 marks], and
iii. suggest a way in which the couple could reduce their overall interest
payments [1 mark]

I have only this left pliz help me

Answer 1

step 1:
the actual mortgage will be .8(360,000) = 288,00

step2: initial monthly payment
i = .05/12 = .00416666...
n = 12*25 = 300
288000 = paym(1 - 1.004166..^-300)/.0041666...
paym = $1,683.62

But they missed the first 12 payments. We must assume that the bank will still get their interest, (of course they would!)
Amount owing after 1 year without making any payments
= 288000(1.0041666...)^12 = 302,734.63
So you want find the new payments for this amount for a term of 24 years:
new payment:
302734.63 = p(1 - 1.0041666^-288)/.0041666
p = 1807.02

amount owing after the first 5 years, (paying only for 4 years)
= 302734.63(1.00416666..)^48 - 1807.02(1.0041666...^48 - 1)/.00416666..
= $273,808.34

At this point the question becomes really unrealistic, .... their rate increases by 5% each 5 years ?????

So now you would have a new balance of 273,808.34
with i = .10/12 = .008333..
n = 240

new payment for remaining 20 years:
p(1 - 1.0083333..^240/)/.0083333.. = 273.808.34
payment = p = 2642.31

repeat the steps to find the outstanding balance after these 5 years
273808.34(1.0083333..)^60 - 2642.31(1.0083333..^60 - 1)/.0083333..
= .....

now increase the interest rate to 15% (????) and repeat the previous steps

Crazy Question!!!

The last part becomes really weird.
You will have an outstanding balance after 20 years, and a new calculated payment. But you will double this, so you should have something like this:
outstanding balance = (the doubled payment)(1 - (1+rate)^-n)/new rate

you will have use logs to find n.
n will assuredly come out as a decimal, the rounded down value of n will be the number of whole payments you need.