Question 1

A loan of $54 000.00 is repaid by making payments of $3000.00 at the end of every three months. If the interest is 9% compounded monthly, calculate how long the payments have to be made.

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Question 2

Note: The calculations for this question were done using Excel's RATE function.
A $160 000.00 mortgage with a 20-year term is repaid by making monthly payments of $1361.00. What is the rate of interest compounded semi-annually on the mortgage?

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Question 3

Note: The calculations for this question were done using Excel's RATE function.
A $345 000.00 mortgage is repaid in 19 years by making monthly payments of $2486.44. What is the nominal annual rate of interest compounded semi-annually?

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Question 4

Calculate the accumulated value after ten years of payments of $1000.00 made at the end of each year if interest is 6% compounded monthly.

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Question 5

For how long must $179.23 be deposited at the end of each month to accumulate to $9700.00 at 6.18% compounded quarterly?

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Question 6

Note: The calculations for this question were done using Excel's RATE function.
A property worth $15 000.00 is purchased for 10% down and semi-annual payments of $1750.00 for twelve years. What is the effective rate of interest if interest is compounded semi-annually?

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Question 7

What is the final amount of an investment where you are making quarterly deposits of $672.31 at the end of the payment period for 7 years and 9 months? The interest rate is 6.16% compounded semi-annually.

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Question 8

A $360 000.00 mortgage is amortized by making monthly payments of $2600. If interest is 7.5% compounded semi-annually, what is the term of the mortgage?

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Question 9

Calculate the accumulated value after twenty years of payments of $12000.00 made at the end of each year if interest is 6% compounded semi-annually.

Accepted Answer

The correct calculation involves using the formula for the future value of an annuity, which accounts for regular payments (PMT) made at the end of each period and the compounding interest rate. Given that the interest is compounded semi-annually but payments are made annually, we adjust the interest rate for the annual payments. The formula for the future value of an annuity is FV = PMT * [((1 + r)^n - 1) / r], where PMT is the annual payment, r is the annual interest rate (expressed as a decimal), and n is the total number of payments. Here, PMT = $12,000, r = 6% or 0.06 (annual interest rate), and n = 20 (years). However, because the interest is compounded semi-annually, we use the effective annual rate (EAR) for the calculation, which still aligns with the formula since payments are annual. Plugging the values into the formula or using a financial calculator with these inputs gives us the future value closest to choice A, $445,721.73.

Question 10

Note: The calculations for this question were done using Excel's RATE function.
What is the rate of interest compounded quarterly if a loan of $31 500.00 is repaid in seven years by payments of $2712.00 made at the end of every six months?

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Question 11

How much should you invest today into account paying 3.2% compounded quarterly if you want to be able to withdraw at the end of every 3 month the amounts of money growing at a constant rate of 3% for the period of 5 years, if the first withdrawal is to be $100 five years three months from now?

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Question 12

Note: The calculations for this question were done using Excel's RATE function.
What nominal annual rate of interest compounded semi-annually is earned by quarterly deposits of $7327.00 made for six years if the balance just after the last deposit is $289 000.00?

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Question 13

Mr. Lavergne accumulated $320 000.00 in an RRSP. He converted the RRSP into an RRIF and started to withdraw $7500.00 at the end of every three months from the fund. If interest is 4.68% compounded monthly, how many withdrawals can Mr. Lavergne make?

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Question 14

Sabrina deposits $300.00 into a savings account at the end of each month for five years. If the accumulated value of the deposits is $20 000.00 and interest is compounded semi-annually, calculate the nominal rate of interest

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Question 15

You miss the 11th to 13th payments of a loan. The loan payments are $519.27 each month and the interest rate is 8.45% compounded annually. How much are you behind in your payments on the day that you miss the 13th payment?

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Question 16

Deon makes monthly contributions of $250.00 at the end of every month into an RRSP. Calculate, to the nearest month, how long it will take to grow to $100 000.00 if interest is 8% compounded annually.

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Question 17

For their daughter's future education David and Bonie set a fund in which they invest at the end of every six months. The first investment is $100 and they plan to increase their investments at a constant rate of 0.5%. If the fund earns 2 .4% compounded semi-annually, how much money will be in the fund in 16 years when their daughter goes to college?

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Question 18

Calculate the nominal interest rate of interest compounded quarterly if a loan of 43 000.00 is repaid in seven years by payments of $4000.00 made at the end of every six months.

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Question 19

Mr. Sepaba accumulated $600 000.00 in an RRSP. He converted the RRSP into an RRIF and started to withdraw $3000.00 at the end of every month from the fund. If interest is 4.5% compounded yearly, for how long can Mr. Sepaba make withdrawals?

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Question 20

Note: The calculations for this question were done using Excel's RATE function.
Compute the nominal annual rate of interest on a loan of $67 000.00 repaid in semi-annual installments of $6540.00 in 11.5 years.

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Quiz 12: Ordinary General Annuities

A loan of $54 000.00 is repaid by making payments of $3000.00 at the end of every three months. If the interest is 9% compounded monthly, calculate how long the payments have to be made.

Note: The calculations for this question were done using Excel's RATE function. A $160 000.00 mortgage with a 20-year term is repaid by making monthly payments of $1361.00. What is the rate of interest compounded semi-annually on the mortgage?

Note: The calculations for this question were done using Excel's RATE function. A $345 000.00 mortgage is repaid in 19 years by making monthly payments of $2486.44. What is the nominal annual rate of interest compounded semi-annually?

Calculate the accumulated value after ten years of payments of $1000.00 made at the end of each year if interest is 6% compounded monthly.

For how long must $179.23 be deposited at the end of each month to accumulate to $9700.00 at 6.18% compounded quarterly?

Note: The calculations for this question were done using Excel's RATE function. A property worth $15 000.00 is purchased for 10% down and semi-annual payments of $1750.00 for twelve years. What is the effective rate of interest if interest is compounded semi-annually?

What is the final amount of an investment where you are making quarterly deposits of $672.31 at the end of the payment period for 7 years and 9 months? The interest rate is 6.16% compounded semi-annually.

A $360 000.00 mortgage is amortized by making monthly payments of $2600. If interest is 7.5% compounded semi-annually, what is the term of the mortgage?

Calculate the accumulated value after twenty years of payments of $12000.00 made at the end of each year if interest is 6% compounded semi-annually.

Note: The calculations for this question were done using Excel's RATE function. What is the rate of interest compounded quarterly if a loan of $31 500.00 is repaid in seven years by payments of $2712.00 made at the end of every six months?

How much should you invest today into account paying 3.2% compounded quarterly if you want to be able to withdraw at the end of every 3 month the amounts of money growing at a constant rate of 3% for the period of 5 years, if the first withdrawal is to be $100 five years three months from now?

Note: The calculations for this question were done using Excel's RATE function. What nominal annual rate of interest compounded semi-annually is earned by quarterly deposits of $7327.00 made for six years if the balance just after the last deposit is $289 000.00?

Mr. Lavergne accumulated $320 000.00 in an RRSP. He converted the RRSP into an RRIF and started to withdraw $7500.00 at the end of every three months from the fund. If interest is 4.68% compounded monthly, how many withdrawals can Mr. Lavergne make?

Sabrina deposits $300.00 into a savings account at the end of each month for five years. If the accumulated value of the deposits is $20 000.00 and interest is compounded semi-annually, calculate the nominal rate of interest

You miss the 11th to 13th payments of a loan. The loan payments are $519.27 each month and the interest rate is 8.45% compounded annually. How much are you behind in your payments on the day that you miss the 13th payment?

Deon makes monthly contributions of $250.00 at the end of every month into an RRSP. Calculate, to the nearest month, how long it will take to grow to $100 000.00 if interest is 8% compounded annually.

Calculate the nominal interest rate of interest compounded quarterly if a loan of 43 000.00 is repaid in seven years by payments of $4000.00 made at the end of every six months.

Mr. Sepaba accumulated $600 000.00 in an RRSP. He converted the RRSP into an RRIF and started to withdraw $3000.00 at the end of every month from the fund. If interest is 4.5% compounded yearly, for how long can Mr. Sepaba make withdrawals?

Note: The calculations for this question were done using Excel's RATE function. Compute the nominal annual rate of interest on a loan of $67 000.00 repaid in semi-annual installments of $6540.00 in 11.5 years.