A couple negotiated with a vendor and purchased a two-bedroom house
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
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.
Sure, I can help you with that.
(a) To calculate the sale price of the house, we need to determine the total loan amount and the down payment made by the couple.
The loan amount is given as $360,000, which is 80% of the sale price. We can then calculate the sale price by dividing the loan amount by 80% (or multiplying by 1.25):
Sale Price = Loan Amount / 80% = $360,000 / 0.80 = $450,000
Therefore, the sale price of the house is $450,000.
To calculate the down payment, we know that the bank required a compulsory 20% down payment. We can calculate the down payment as a percentage of the sale price:
Down Payment = 20% * Sale Price = 20% * $450,000 = $90,000
Therefore, the couple made a $90,000 down payment to qualify for the loan.
(b) The monthly payment applicable in the first 5-year period, accounting for the first 12 months of missed payments, can be calculated using an amortization formula. The formula is:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))
The Monthly Interest Rate can be calculated by dividing the annual interest rate by 12 (since it is a monthly rate). In this case, the annual interest rate is 5%, so the Monthly Interest Rate is 5% / 12 = 0.4167%.
The Number of Payments can be calculated by multiplying the number of years by 12 (since there are 12 months in a year). In this case, the number of years is 5, so the Number of Payments is 5 * 12 = 60 payments.
Using these values in the formula, we can calculate the monthly payment for the first 5-year period:
Monthly Payment = ($360,000 * 0.4167%) / (1 - (1 + 0.4167%)^(-60))
After calculating this, you can also deduct the missed payments for the first 12 months.
(c) To calculate the new monthly payments applicable in each 5-year period, we need to consider the increasing interest rate after every 5 years.
For the first 5 years, we already calculated the monthly payment in part (b).
For the next 5-year period (6th to 10th year), the interest rate will increase by 5%. To calculate the new monthly payment, you can use the same amortization formula as in part (b), but with the updated interest rate.
For the 11th to 15th year, the interest rate will increase by another 5% from the previous period. Again, you can use the amortization formula with the updated interest rate.
Repeat this process for the 16th to 20th year and the 21st to 25th year.
(d) To compute the number of full payments that the couple will make in the final 5 years of the loan term, we need to divide the remaining loan balance by the doubled repayment amount per month.
The remaining loan balance can be calculated using the amortization formula, considering the number of payments that have already been made until the start of the final 5-year period.
Once you have the number of full payments for the final 5 years, you can subtract this from the total number of payments in the term to determine the partial payment necessary to conclude the loan repayments.
To reduce overall interest payments, the couple can consider making additional principal payments whenever possible. This will help reduce the total outstanding balance and therefore decrease the interest paid over the loan term. They should check with their bank if there are any restrictions or penalties for making additional payments.