^[88] Five years ago, the Smiths purchased a home in North Vancouver for $650,000. They made a down payment of exactly 20% and mortgaged the balance with Westminster Savings Credit Union. The interest rate was 5.6%, compounded semi-annually, for a 5-year term, amortized over 25 years.

a. Calculate the size of the monthly payment required. The credit union rounds the payment up to the next dollar.

b. What percentage of the original mortgage was paid off in the first 3 years?

c. How much interest did the Smiths pay in the fourth year of the mortgage?

d. The Smiths, after having made 5 years of payments, made a lump-sum payment to reduce the outstanding balance to $450,000. What was the amount of the lump-sum payment?

e. After making the lump sum payment, the Smiths renew their mortgage for another 5-year term, amortized over the remaining time, at 6.8%, compounded semiannually. Calculate the new monthly payment. Round the payment up to the next dollar.

f. Assuming the interest rate remains the same over the remaining time, what is the size of the final payment?

 

^[89] In October 2012, the Reids obtained a mortgage for $380,000 at 6.8% interest compounded semiannually, for a 5-year term, amortized over 25 years. (The bank rounds the payment up to the next dollar.) Today, (October 2017), they have decided to increase the size of their mortgage and use the money for house renovations. How much more money can they borrow if they want to keep the same monthly payment as before but still pay off the mortgage by October 2037 (twenty years from now)? The interest rate has fallen to 4.3%, compounded semiannually for a five-year term.

 

^[90] You purchase a new car. The dealer offers you terms of 20% down and the remainder financed over five years at an interest rate of 8% compounded monthly.

a. Find the size of your monthly payment if your first payment is due at the end of the month and the price of the car was $33,906.25, including GST, PST, documentation fee, and government environmental levies.

b. What is the cost of financing (how much interest will you pay over the life of the loan)?

 

^[91] You would like to save for your retirement by making monthly deposits of $200 into an account. What nominal interest rate of interest, compounded monthly, must you earn to accumulate $1,000,000 in thirty years? Assume that the first payment will be at the end of the month.

 

^[92] You are considering quitting smoking due to the high cost of a pack of cigarettes. You smoke 1 pack a day at a cost of $7.50. If you put the $7.50 you would have spent on cigarettes into a savings account earning 5.75% interest compounded daily, how much would you have in the bank at the end of ten years?

 

^[93]  Upon graduation, you have a student loan of $15,000. The most you can afford to pay is $550 per month. How long will it take you to repay the loan with payments of $550 per month starting in one month if the interest rate is 6% compounded monthly?

 

^[94] Kent sold his car to Carolyn for $1,000 down and monthly payments of $120.03 at the end of every month for 3.5 years. The interest rate charged is 12%, compounded monthly. What was the selling price of the car?

 

^[95] Rajinder bought a car with $5,000 down, followed by equal monthly payments of $783.41 at the end of every month for 2 years at 16% compounded monthly.

a. What is the selling price of the car?

b. What is the cost of financing?

 

^[96] Manpreet paid $14,000 to buy a used car. He made a down payment followed by equal monthly payments of $249.50 at the end of every month for 4 years at 8% compounded monthly.

a. What is the size of the down payment?

b. What is the cost of financing?

 

^[97] For $42,000, an individual can purchase a 5-year annuity from Continental Life and receive monthly payments of $871.85 for 5 years, with the first payment one month from now. What effective rate of interest does this investment earn?

 

Deferred Perpetuities

^[98] A scholarship fund is to be set up. The fund will pay out a scholarship of $20,000 every year, with the first scholarship paid out two years after the fund is set up. Find the size of the donation needed. Assume the fund will earn 10% effective.

 

^[99] A bursary fund for BCIT honors students is to be funded by a perpetual fund. The fund earns interest at 10% compounded annually and is to pay $30,000 each year, with the first payment four years after the fund is set up. Find the size of the initial funding that is required.

 

^[100] An alumnus wants to donate a sum of money to his Alma Mater that will provide a scholarship of $750.00 every six (6) months in perpetuity. If money can be invested at 6% compounded semi-annually and the first $750.00 is to be awarded at the end of one year, how much must he donate to the school today?

 

^[101] You are considering purchasing shares of New Wave Technology Corp. The company has stated that they will pay dividends of $0.72 per share every three (3) months, with the first dividend paid exactly four (4) years from today. If the current interest rates are 8% compounded quarterly, what would you be willing to pay for one share today?