Question

Mini-Case B

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.

Part 1 (1 mark)

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?

Calculation of Minimum Emergency Fund Suitable Investment

Part 2 (1 mark)

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.

LOC Payment Calculation Impact of Non-Payment

Part 3 (1 mark)

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

Calculation of Mortgage Payment and Balance after 34 Months (rounded)

Part 4

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.

Month	$ Beg. Bal.	$ Pmt.	$ Interest	$ Principal	$ End. Bal.
35
36
37
38

Part 5 (1 mark)

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?

Calculation of Total Interest Owed at the end of 4 months Repay or add to the mortgage balance?

Answer 1

Part-1

Excluding the balance on their LOC--Minimum Emergency Fund should be $ 7000 to meet monthly living expenses.

Suitable Investment will be those that pay monthly annuities, ie.fixed amounts at fixed intervals -- to meet the basic living expenses

Part-2

LOC Payment Calculation---8520*(3%+0.5%)=$ 298.2

Impact of Non-Payment

Not making the payment ,will certainly affect the credit-rating of the card-holder , assigned by the lender . Also future interest rates for a probable-to- default-borrower , may be higher than for others. The lender will red-mark such a borrower & have a keen watch , to ensure he pays all the installment, in time.

Part-3

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

Balance after 34 Months=

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

Part 4

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

Month	$ Beg. Bal.	$ Pmt.	$ Interest	$ Principal	$ End. Bal.
35	477654	3106	1422	1683	475971
36	475971	3106	1417	1688	474282
37	474282	3106	1412	1693	472589
38	472589	3106	1407	1698	470891

Part 5

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.

Calculation of Total Interest Owed at the end of 4 months = $ 5683

Repay or add to the mortgage balance-- Repay