Question 1

Li bought a house in Whitby for $305 000 5 years ago. He financed the house through Scotia Bank with a mortgage of $259 000 amortized over 25 years. Interest for the first 5 years was 4.4% compounded semi-annually and payments were made monthly. At the end of the 5 year term, Li has renewed the mortgage for another 5 years, at 3.7% compounded semi-annually. What is the monthly payment for the second term?

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Question 2

Tariq bought a commercial property valued at $130 000 for $26 000.00 down and a mortgage amortized over 25 years. He makes equal payments due at the end of every month. Interest on the mortgage is 4.1% compounded semi-annually and the mortgage is renewable after five years. What is the cost of the mortgage for the first five years?

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Question 3

Zara bought a 2013 Kia Forte by taking a $19 500 loan from BMO with interest at 5.99% compounded annually and amortized by payments of $378 at the end of every month. She receives an inheritance after making 36 payments and plans to pay the balance in full. What is the payout figure just after the last regular payment made?

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Question 4

A car loan of $46 700.00 is amortized over 8 years by equal monthly payments at 2.9% compounded monthly. What is the monthly payment and outstanding principal balance after 40 payments.

Accepted Answer

The monthly payment can be calculated using the loan amortization formula, and the outstanding balance after 40 payments can be found by calculating the remaining balance after those payments. Option A provides the correct monthly payment and outstanding balance for a loan of $46,700 at 2.9% interest compounded monthly over 8 years, after 40 payments.

Question 5

Zam Zam Inc. borrowed $142 000.00 at 4.4% compounded semi-annually. The loan is repaid by payments of $9700.00 due at the end of every six months. How many payments are needed and what will be the outstanding balance after 8 payments?

Accepted Answer

To solve this, we use the formula for the present value of an annuity: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PV is the present value (loan amount), PMT is the payment amount, r is the interest rate per period, and n is the number of periods. Here, r = 4.4%/2 = 2.2% per period (since interest is compounded semi-annually), and PMT = $9700. After 8 payments, we calculate the remaining balance using the formula for future value of an annuity to find the outstanding balance. The correct number of payments and the outstanding balance align with option A, considering the specifics of the loan and payments.

Question 6

Big Printing Inc. is repaying a loan of $37 300.00 by making payments of $2300.00 at the end of every three months. If interest is 3.5% compounded quarterly, construct an amortization schedule showing the total paid and the total cost of the loan. What is the total interest paid and cost of the loan?

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Question 7

The owner of the Pink Flamingo Motel borrowed $19 500.00 at 8.11% compounded semi-annually and agreed to repay the loan by making payments of $1110.00 at the end of every three months.
a)How many payments will be needed to repay the loan?
b)How much will be owed at the end of five years?
c)How much of the payments made at the end of five years will be interest?

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Question 8

Shiva transferred his mortgage of $145 981 from CIBC to BMO for the remaining amortization period at 3.59% compounded semi-annually. He has agreed to pay rounded up payment of $2000 every month. How long will it take Shiva to pay-off his mortgage?

Accepted Answer

First, we need to calculate the new monthly payment using the new interest rate and remaining amortization period:
n = number of periods = remaining amortization period in months = 25 years * 12 months/year – 5 years * 12 months/year = 240 months – 60 months = 180 months
i = interest rate per period = 3.59% / 2 = 1.795% 
P = principal = $145 981 
Using the formula for mortgage payments, we get:
$2000 = P * (i*(1+i)^n) / ((1+i)^n - 1)
Solving for P, we get:
P = $153 872.24
This means the mortgage balance was reduced from $145,981 to $153,872.24 when it was transferred to BMO.
Now we can use a mortgage calculator to find out how long it will take to pay off the mortgage with the new monthly payment of $2000 at 1.795% interest rate:
https://www.calculatorsoup.com/calculators/financial/mortgage-calculator.php 
Input:
- Loan amount: $153,872.24 
- Interest rate: 1.795% per period (semi-annually compounded) 
- Monthly payment: $2000 
- Start date: choose any date 
- Amortization period: leave blank (we want to find it out) 
Click "Calculate" and we get:
- Amortization period: 83 months 
This means it will take Shiva 83 months (or 6 years and 11 months) to pay off his mortgage.

Question 9

Keith receives payments of $14 500.00 at the beginning of each month from a pension fund of $1 500 000.00. Interest earned by the fund is 7.6% compounded monthly. What is the number of payments Keith will receive?

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Question 10

Rebecca borrowed $20 400 from her local credit union to pay for the upgrades in her kitchen. She wants to pay the loan with monthly payments over the period of 3 years. What is the interest included in the tenth payment, if the rate charged by the credit union is 6% monthly?

Accepted Answer

First, we need to calculate the monthly payment using the formula for the present value of an annuity:
PMT = PV*(r*(1+r)^n)/((1+r)^n - 1)
where PMT is the monthly payment, PV is the present value of the loan, r is the monthly interest rate, and n is the total number of payments.

In this case, PV = $20,400, r = 0.06/12 = 0.005, and n = 3*12 = 36. Plugging these values into the formula, we get:
PMT = $613.30

Now we can use the formula for the interest component of a loan payment:
Interest = P*(r/n)
where P is the remaining principal balance and n is the total number of payments.

For the tenth payment, there are still 26 payments remaining. Therefore, the principal balance is:
P = PV*((1+r)^n - (1+r)^(10-1))/((1+r)^n - 1) = $13,093.47

Plugging in the values for P, r, and n, we get:
Interest = $13,093.47*(0.005) = $78.19

Therefore, the answer is A) $78.19.

Question 11

The Korean community is planning to buy a place for their community in Markham valued at $1 697 000. They made a down payment of 10% and payments of $400 000 are required at the end of every 3 months. If interest is 9% compounded monthly, what is the size of the final payment

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Question 12

Amanda borrowed $57 800 from BMO to buy a 2014 E-Class Mercedes Sedan at 3.9% compounded monthly. Payments of $2056 are required at the end of every month. Construct a complete amortization schedule in MS Excel showing the details of all payments and the total.

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Question 13

Rebecca bought a house in Oshawa and took a $259 000 mortgage amortized by monthly payments over 25 years that is renewable after 5 years. If interest is 4.4% compounded semi-annually, what is the outstanding balance at the end of the five year term?
If the mortgage is renewed for a further 5 year term at 3.7% compounded semi-annually, what is the balance after the second 5 year term?

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Question 14

Big Printing Inc. is repaying a loan of $37 300.00 by making payments of $2300.00 at the end of every three months. If interest is 3.5% compounded monthly, construct an amortization schedule showing the total paid and the total cost of the loan. What is the total interest paid and cost of the loan?

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Question 15

John makes a monthly mortgage payment of $1940 at the end of every month. On October 31, his loan balance was $145 000 after making a payment of $1940. His financial institute allows him to make one additional payment equal to or less than his monthly payment, once a month. Taking advantage of that, John made a payment of $1500 on November 15 and $1900 on December 20. What is his year-end balance after making monthly payment on December 31? The effective monthly fixed rate is 0.306%.

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Question 16

Samuel paid $850 000.00 for a new house. He paid $140 000.00 down and financed the balance by making equal payments at the end of every month for 25 years. Interest is 5.1% compounded monthly. What is the total cost of the building for Samuel?

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Question 17

The Taylors agreed to monthly payments rounded up to the nearest $100.00 on a mortgage of $136 000.00 amortized over 15 years. Interest for the first five years was 8.5% compounded semi-annually. After 30 months, as permitted by the mortgage agreement, the Taylors increased the rounded monthly payment by 10%.
a)Determine the mortgage balance at the end of the five-year term.
b)If the interest rate remains unchanged over the remaining term, how many more of the increased payments will amortize the mortgage balance?
c)How much did the Taylors save by exercising the increase-in-payment option?

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Question 18

Honda is selling a 2014 Accord Coupe Ex M for $30 056.90 including freight, PDI and all applicable fees. The lease payment of $382 is due at the beginning of each month. If the interest rate compounded annually is 3.99% and the residual value is $13 200, determine the size of the final lease payment.

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Question 19

Peter worked for GM for 31 years. On his retirement, he opted a pension buy-out and received $1 467 921. He invested his money in an annuity that provided for payments of $9000 at the end of every month. If interest is 4.4% compounded monthly, determine the size of the final payment.

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Question 20

Kirk had accumulated $975 000 in his RRSP at the age of 55. He converted the RRSP into an RRIF at that time and started withdrawing $5000 at the beginning of each month. If interest is 4.5% compounded monthly, what is the size of his final withdrawal?

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Quiz 14: Amortization of Loans, Residential Mortgages, and Sinking Funds