Question

The Simpsons, owners of a spa on the island of Montreal, have been hard-hit by the pandemic. Before they were forced to close their spa, their take home income, after taxes but before living expenses, was $7,000 a month. The Simpsons spent all of their take-home cash flow and even more, by borrowing on a line of credit (LOC). The day their spa was closed the balance on their LOC was $8,520. Normally they use the LOC to clear the balance on their several credit cards each month. Terms of the LOC include a repayment of 3% of principal every month plus interest charged at a rate of 0.5% per month. Three years ago the Simpsons took out a $532,000 mortgage to purchase a home in Beaconsfield. Payments are monthly at a rate of 3.6%, compounded semi-annually. The original amortization period was 20 years and they have made 34 payments to date. The Simpson’s mortgagor has offered them the possibility of suspending payments for the next 4 months. Nevertheless, they will still owe the interest they would have paid on each payment. Furthermore, the future value of the unpaid interest after 4 months will mean that they will have to pay interest on the outstanding interest should they take up this offer.

a) Excluding the balance on their LOC, what minimum emergency fund should the Simpsons have held to meet unforeseen events?  What type of investment would be suitable for such a fund?

b) How much would the couple have to pay on the LOC for the month following closure of their spa?  What impact would not making the payment have on their credit rating?  Please explain.

c) What is the monthly payment on the Simpson’s mortgage?  What is the balance after 34 months?  Round to the nearest dollar

d) Draw up the Simpson’s mortgage amortization table for the next four months (i.e. for payments 35-38).  Their monthly mortgage rate is 0.2978%.  Round to the nearest dollar.

e) How much interest will the Simpsons owe at the end of the 4-month period?  (Mortgage payments are made at the end of the month.)  Round to the nearest dollar.  Remember, they will be obliged to pay interest on their interest. If they are given the choice of adding this to their mortgage balance or paying it immediately in cash, what would you recommend, and why?

Answer 1

a. they should have held a fund that pays atleast $ 7000 per month for their living expenses.

Investments that pay monthly annuities , ie. Fixed sums at monthly intervals , would have been preferable.

b) Amount the couple would have to pay on the LOC for the month following closure of their spa=

(8520*(3%+0.5%))=

298.2

Not making the payment ,will certainly affect the credit-rating o the card-holder ,by the lender & also future interest rates for the defaulting borrower , may be higher than for others. He is definite to be red-marked & watched over, if he misses any installment.

c)Monthly payment on the Simpson’s mortgage

Monthly payment=PV of mortgage/Annuity Factor,i=0.2978%(given in d.); n=20*12=240

ie. 532000/((1-1.002978^-240)/0.002978)=

3105.54

Mortgage principal Balance after 34 months=

FV of original balance at end Mth 34 -FV of annuity at end mt. 34

ie. (Original Loan amt.*(1+r)^n)-(Mthly.pmt.*((1+r)^n-1)/r)

Plugging in the variables, in the above formula,

ie. (532000*(1+0.002978)^34)-(3105.54*((1+0.002978)^34-1)/0.002978)=

477654

d)Simpson’s mortgage amortization table for the next four months (i.e. for payments 35-38).  Their monthly mortgage rate is 0.2978%.

Mth.	Mthly pmt.	Tow. Int.	Tow. Mort.	Mort. Bal.
34				477654
35	3106	1422	1683	475971
36	3106	1417	1688	474282
37	3106	1412	1693	472589
38	3106	1407	1698	470891

e.

Interest the Simpsons will owe at the end of the 4-month period--they are obliged to pay interest on their interest, if they take up the mortgagor's offer of mortgage- payments suspension for the next 4 months---instead of the normal end-of-mth, mortgage payments --- rounded to nearest $

Sum of future values of month 35-38 interest amounts as in Table in Part-4

ie.(1422*1.002978^3)+(1417*1.002978^2)+(1412*1.002978^1)+1407=

5683

If they are given the choice of adding this to their mortgage balance or paying it immediately in cash, they should pay in cash immediately--otherwise, again interest to be paid will be compounded, ie. Interest needs to be paid on interest.