^[74] You purchase 500 preferred shares of Yardmucks Coffee that pay a quarterly dividend of $0.26 per share. The next dividend is due in 3 months. Current interest rates are 8% compounded quarterly.

a. What would you be willing to pay for the 500 shares?

b. If interest rates drop to 6.5% compounded quarterly, how much would you expect to gain or lose if you sell all of your shares? Note: the next dividend is due in 3 months and the dividend per share is still $0.26.

 

^[75] The Winfall lottery offers you two choices for its grand prize. Either a cash prize of $1,500,000 today or $7,000 per month forever (with the first installment one month from now).

a. Which choice should you select if interest is 6% compounded monthly?

b. You choose the $1,500,000 today and deposit it into an account earning 6% compounded monthly. How much could you withdraw each month forever? Assume the first withdrawal is one month from now.

 

^[76] You borrow $50,000 and agree to make monthly payments for 15 years starting one month later. Calculate the size of your payments if the interest rate is 9% effective.

 

^[77] You borrow $20,000 today from a moneylender called The Money Branch. As a result of your bad credit, The Money Branch charges you an interest rate of 28.8%. You will repay the loan with equal monthly payments over four years, with the first payment one month from now.

a. Find the size of the monthly payment if the interest is: (i)28.8% compounded monthly or (ii) 28.8% compounded semiannually.

b. How much less interest would you pay if they compound the interest semiannually, instead of monthly?

 

^[78] The University of Edmonton received a donation from a wealthy individual. Some of the donated money will be set aside to create a scholarship fund that will pay out $10,000 at the end of every 6 months, in perpetuity. If the invested funds can earn 8% compounded semi-annually, instead of 5% compounded semi-annually, how much less money must they set aside today to pay out a $10,000 scholarship?

 

^[79] You purchase 200 preferred shares of Black Bear Brewing that pay a dividend of $1 per share every 3 months. Current interest rates are 12% compounded monthly. The next dividend is due in 3 months.

a. How much would you be willing to pay for the 200 shares?

b. If interest rates fall to 8% compounded quarterly, how much would you expect to gain or lose if you sell all of your shares? Note: the next dividend is due in 3 months and the dividend per share is unchanged.

 

Mortgages

^[80] You take out a $200,000 mortgage:

a. What is the periodic interest rate per month if the rate is

i. 12% compounded monthly?

ii. 12% compounded semi-annually?

b. If you borrow $200,000, how much interest is paid in the first month? Use both rates and compare your answers.

 

^[81] A debt of $1,200 is repaid by monthly payments of $350 at the end of each month. The interest rate is 12% compounded monthly. Construct the complete amortization schedule without using the AMRT keys. Then go back and verify all the answers using the AMRT and  Pl/P2 keys.

Period	Payment  PMT	Interest  INT	Principal Paid  PRN	Balance Owing  BAL
0
1
2
3
4
TOTALS

 

^[82] You purchase a house in Surrey for $220,000 and put 25% down so you could receive a conventional mortgage. You decide to get your mortgage at Superstore since they give you free groceries each year as an incentive. A 5-year term mortgage (i.e., the interest rate is fixed for 5 years) is negotiated with Simplii Financial, in which the balance is amortized over 20 years (repaid with equal payments over 20 years) at 6.70% interest compounded semi-annually.

 

a. Calculate your monthly payment. The bank rounds up the payment to the next dollar.

b. COMP n to verify that n is slightly smaller than 240. If the value of n = -100, then you forgot to make the payment negative. If the value of n is exactly 240, then you forgot to re-enter the payment.

c. Find out how the first payment is distributed between interest and principal. Compare this to the results for the 60th payment.

d. How much interest did you pay in the first year? By how much was the balance outstanding reduced in the first year?

e. What percent of the original mortgage was paid off in the first two years?

f. How much principal was paid off in the first five years? How much interest did you pay in the first five years?

g. How much interest did you pay in the fifth year of the mortgage? How much principal was repaid in the fifth year?

h. How much will you still owe after you have made five years of payments?

i. Calculate the value of the final payment assuming that the interest rate never changes during the 20 years.

 

^[83] The Archibalds are eligible for a Canada Mortgage and Housing Corp. insured mortgage, allowing them to qualify for a mortgage of up to 95% of the selling price of the house. They are also subject to the 30% rule: no more than 30% of their gross income can go towards paying the mortgage and property taxes.

a. What is the maximum mortgage they qualify for if their gross monthly income is $5,000 and they want to amortize the mortgage over 25 years? Assume that the property taxes on the house are $1,800 per year (after the homeowner’s grant). Current mortgage rates are 6.80% compounded semiannually. Round answer to the nearest $100.

b. The Archibalds take out a mortgage for $195,000 with Citizen’s Bank, amortized over 25 years at 6.8% interest compounded semiannually for a 5-year term. What is the size of the monthly mortgage payment(round up to the next dollar)?

c. How much interest did they pay in the first five years of the mortgage?

d. How much money would they still owe on this mortgage after five years of payments?

e. When they renew their mortgage in five years time, mortgage rates have fallen to 6.0 % compounded semi­ annually for a five-year term. They have saved $15,000 and will use it to reduce the size of the mortgage. Find the size of their new monthly payments, assuming the balance outstanding is amortized over the remaining time. The bank rounds up the payment to the next dollar.

f. What is the size of the final payment of the renewed mortgage, assuming that the interest rate does not change during the remaining 20 years?

 

^[84] Banks normally use the 30% rule: no more than 30% of your gross income can go towards paying your mortgage and property taxes.

a. If your gross monthly income is $4,000 per month and your property taxes are $2,400 per year (after the $470 homeowners’ grant), what is the largest mortgage a bank would authorize if the mortgage is amortized over 25 years and the rate of interest is 7.45% compounded semiannually? Round answer to the nearest $100. (Assume monthly payments).

b. You purchase a fixer-upper house in downtown Mission for $164,000. Your down payment is 25%, and you negotiate a first mortgage for the balance. The mortgage is at 7.45%, compounded semi-annually, amortized over 25 years for a 3-year term. How large a monthly payment is required? The bank rounds payment up to the next dollar.

c. How much interest did you pay in the first three years of the mortgage?

d. What percent of the original mortgage have you paid off in the first three years?

e. How much interest did you pay in the third year only?

f. In three years, the term of your mortgage is up, and you wish to renew. Interest rates have increased to 9.25% compounded semiannually for a three-year term mortgage. At this time, you make a lump-sum payment of $10,000 to reduce the size of your mortgage. Calculate the size of the new monthly payments, assuming the balance outstanding is amortized over the remaining time. Round up to the next dollar.

g. What is the size of the final payment of the renewed mortgage, assuming that the interest rate does not change during the remaining 22 years?

 

^[85]  Suppose you take out a mortgage amortized over 25 years for $179,940 at j2 = 12.5%.

a. Find the size of the monthly payment. Round payment to the nearest penny.

b. How much time and money would you save if you made 26 bi-weekly payments (equal to half of the monthly payment) instead of twelve monthly payments each year? Assume that the interest rate never changes during the 25 years.

 

^[86]       In March 2012, the Beckers purchased a house in Delta for $512,500. They made a down payment of exactly 20% and took out a mortgage with TD Canada Trust for the balance at an interest rate of 7.5% compounded semi-annually, for a 5-year term, amortized over 25 years.

a. What is the size of the monthly payment? The bank rounds the payment up to the next dollar.

b. How much of the 30th payment was interest?

c. How much interest did the Beckers pay in the 3rd year of the mortgage?

d. Today, (March 2017), they have decided to increase the size of their mortgage and use the money for house renovations. How much extra money can they borrow if they want to keep the same monthly payment as before but still pay off the mortgage by March 2037 (twenty years from now)? The interest rate has fallen to 5.1%, compounded semiannually for a five-year term.

e. The Beckers increase their mortgage to $450,000 and amortize it over 20 years at 5.1%, compounded semi­ annually. What is the size of their monthly payment? (The bank rounds up the payment to the next dollar.)

f. What is the size of the final payment, assuming that the interest rate stays the same over the remaining twenty years?

 

^[87] The Blacks are considering purchasing a three-bedroom townhouse in the Killarney area of Vancouver. Their gross monthly income is $12,000 per month. The property taxes on the townhouse are $3,000 per year, and they also have to pay a monthly maintenance fee of $150 per month for the upkeep on the townhouse complex. Banks normally use the 30% rule: no more than 30% of your gross income can go towards paying your mortgage, property taxes, and monthly maintenance fees. What is the largest mortgage a bank would authorize if the mortgage is amortized over 25 years and the rate of interest is 5.6%, compounded semiannually? (Assume monthly payments.)