Question

1) The company holds a 6-year loan of $230 000, at 7.5% compounded annually. Payments are made quarterly. After 15 months, the terms of the loan are renegotiated at 5.5%, compounded monthly with monthly payments for the remainder of the 6-year term.
a. Calculate the payment amount for the original loan.
b. Calculate the accumulated value of the original loan principal after 15 months.
c. Assuming that payments had been made, calculate the accumulated value of the payments made in the first 15 months.
d. Calculate the outstanding balance of the original loan after 15 months.
e. Calculate the number of payments in the renegotiated term to repay the loan.

2) Lux Resources purchased equipment in exchange for a promissory note for $450 000, with the agreement to pay $8000 at the end of each month, starting in eight months. Interest on the loan is 7% compounded annually.
In partnership with the equipment manufacturer, Lux has agreed to establish a scholarship for local business students. A fund of $10 000 has been set up, with the interest earned being paid as the annual scholarship amount. Money is worth 5% compounded annually.
a. Calculate the equivalent value of the equipment loan in eight months.
b. How many month-end payments will have to be made?
c. Calculate the maximum payout of the scholarship, assuming it to be a perpetuity.

3) Karim Soltan is shopping for a new vehicle and has noticed that many vehicle manufacturers are offering special deals to sell off the current year’s vehicles before the new models arrive. Karim’s local Ford dealership is advertising 3.9% financing for a full 48 months (i.e., 3.9% compounded monthly) or up to $4000 cash back on selected vehicles.
The vehicle that Karim wants to purchase costs $24 600$24 600 including taxes, delivery, licence, and dealer preparation. This vehicle qualifies for $1800$1800 cash back if Karim pays cash for the vehicle. Karim has a good credit rating and knows that he could arrange a vehicle loan at his bank for the full price of any vehicle he chooses. His other option is to take the dealer financing offered at 3.9% for 48 months.

Karim wants to know which option requires the lower monthly payment. He knows he can use annuity formulas to calculate the monthly payments.

4) Glenn has made contributions of $250 at the end of every 3 months into an RRSP for 10 years. Interest for the first 10 years was 4% compounded quarterly.
a. What is the amount in the RRSP after the first 10 years?
b. After the first 10 years, Glenn stopped making contributions. The interest rate changed to 5% compounded monthly. How much will Glenn have in his RRSP three years after the last contribution?
c. Suppose Glenn then decides to withdraw the money from his RRSP. How much will he be able to withdraw in monthly amounts over the next 10 years?

Answer 1

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