Question 1

If you want to purchase an annuity providing an income of $2000 at the end of each month for five years, how much will it cost if the purchase funds earn 18% compounded monthly?

Accepted Answer

The cost of purchasing an annuity can be calculated using the present value formula for annuities. Given an interest rate of 18% compounded monthly, the monthly interest rate is 18%/12 = 1.5%. The formula for the present value of an annuity is PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the monthly payment ($2000), r is the monthly interest rate (0.015), and n is the total number of payments (5 years * 12 months = 60 payments). Plugging in the values, we get the present value, which is closest to the amount given in option B.

Question 2

If you make 30 semiannual deposits of $2000 into a fund that earns 10% compounded quarterly, how much money will be in the fund two years after the last deposit?

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Question 3

Jasmine won a prize: the right to receive 36 payments of $100 per month with the first payment one month from today. If money is worth 6% compounded monthly, what is the economic value of these payments one year from today?

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Question 4

Quarterly contributions of $700 are made to an RRSP that earns 6% compounded monthly. How much will be in the plan immediately after the twentieth deposit?

Accepted Answer

The correct answer is found using the future value of a series formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount, $r$ is the monthly interest rate, and $n$ is the total number of payments. Given that the interest rate is 6% compounded monthly, $r = 0.06/12 = 0.005$. With quarterly contributions, there are 4 contributions per year, so for 5 years (20 quarters), $n = 20$. Plugging these values into the formula gives the future value immediately after the twentieth deposit. Calculating with $P = 700$, $r = 0.005$, and $n = 20$, we find the future value to be approximately $16,198.55.

Question 5

Omar will contribute $200 to his RRSP at the end of each month for 15 years and then raise his monthly contribution to $500 at the end of each month for the subsequent 20 years. If his investments earn 11.7% compounded monthly, what will be the value of the investments after the last $500 contribution is made 25 years from now?

Accepted Answer

The value of Omar's investments can be calculated using the future value of an annuity formula for each phase of contributions, and then adding the future value of the first phase (after it has grown for the additional 20 years without additional contributions) to the future value of the second phase. First phase (15 years of $200 monthly contributions):$$FV_1 = P \times \frac{(1 + r)^n - 1}{r}$$Where:- $P = \$200$ (monthly contribution)- $r = \frac{11.7\%}{12} = 0.00975$ (monthly interest rate)- $n = 15 \times 12 = 180$ (total number of contributions)$$FV_1 = 200 \times \frac{(1 + 0.00975)^{180} - 1}{0.00975}$$This amount then grows for another 20 years without additional contributions:$$FV_1' = FV_1 \times (1 + r)^{240}$$Second phase (20 years of $500 monthly contributions):$$FV_2 = P \times \frac{(1 + r)^n - 1}{r}$$Where:- $P = \$500$- $n = 20 \times 12 = 240$$$FV_2 = 500 \times \frac{(1 + 0.00975)^{240} - 1}{0.00975}$$The total future value is the sum of $FV_1'$ and $FV_2$. Calculating these values gives a total close to $1,471,930, which matches option C.

Question 6

What amount could you borrow at 6.6% compounded monthly if you can afford to make monthly payments of $775 for 25 years?

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Question 7

A pension fund has to pay out $750,000 to the retirees at the end of every month for the next 50 years. The fund will be earning 9.6% compounded monthly for the first 30 years and 7.2% compounded monthly for the last 20 years. In order to be able to make these payments, how much money would have to be in the pension fund now?

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Question 8

Calculate the present value of a deferred annuity of 20 annual payments of $25,000 each The interest rate is 8.5% compounded annually and the first payment will be made in six years.

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Question 9

Calculate the present value of a deferred annuity of 20 annual payments of $100,000 each The interest rate is 13.5% compounded annually and the first payment will be made 11 years from now.

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Question 10

Samuel has $290,000 in his Retirement Savings Plan right now. He will not be able to make any more contributions to the RSP but he is planning to let the money accumulate until he has enough so that he can take out $3,000 per month for 25 years. How long will he have to wait until he takes out the first $3,000 withdrawal? His investments earn 7.5% compounded monthly.

Accepted Answer

The answer of Samuel has $290,000 in his Retirement Savings...

Question 11

Calculate the equivalent periodic interest rate per payment interval for the following annuity: Monthly payments discounted at 8.4% compounded semi-annually.

Accepted Answer

To find the equivalent monthly interest rate, first convert the semi-annual rate to an annual rate: (1 + 0.084/2)^2 - 1 = 0.084. Then, convert this annual rate to a monthly rate: (1 + 0.084)^(1/12) - 1 ≈ 0.68806%.

Question 12

If $2,000 is invested at the end of every three months, what will be the total value after 10 years? The investments earn 13% compounded annually.

Accepted Answer

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Question 13

What amount would you borrow at 15% compounded annually if your loan payments are $3,800 per month for 10 years?

Accepted Answer

To find the loan amount, use the formula for the present value of an annuity. The monthly payment is $3,800, the annual interest rate is 15% (or 1.25% per month), and the number of payments is 120 (10 years). The calculation gives approximately $244,193.

Question 14

Determine the future value:

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