Question 1

A financial institution is offering a 3 year rate optimizer GIC with annual rates of 4.6%, 5.2% and 5.8%. If $10,000 was invested in the GIC, then determine the total interest earned at the end of the 3 year period.

Accepted Answer

The answer of A financial institution is offering a 3...

Question 2

Seventeen years after it was first issued at 11% compounded semi-annually, a 30-year, $1,000 strip bond was sold on the bond market at a price that would provide the purchaser with a yield rate of 6.4% compounded semi-annually. What was the selling price at that time?

Accepted Answer

The selling price of the bond can be calculated using the formula for the future value of a present amount at compound interest: $P = P_0(1 + r)^n$, where $P$ is the future value, $P_0$ is the present value (initial investment), $r$ is the interest rate per period, and $n$ is the number of periods. Since the bond is a zero-coupon bond (strip bond), it pays no interest until maturity. The buyer is interested in a yield rate of 6.4% compounded semi-annually for the remaining 13 years (26 periods) of the bond's life. The future value of the bond at maturity (in 13 years) is its face value, $1,000. We rearrange the formula to solve for $P_0$, the present value or selling price: $P_0 = \frac{P}{(1 + r)^n}$. Substituting $P = $1,000$, $r = 0.032$ (6.4% per annum compounded semi-annually gives 3.2% per period), and $n = 26$, we get $P_0 = \frac{1000}{(1 + 0.032)^{26}}$, which calculates to approximately $440.89.

Question 3

A 25-year, $10,000 strip bond was issued at a market rate of 9.4% compounded semi-annually. What was the issue price?

Accepted Answer

To calculate the issue price of a strip bond, we must use the present value formula:

PV = FV / (1 + r/2)^(2n)

Where PV is the present value or issue price of the bond, FV is the face value or maturity value of the bond, r is the market rate or yield to maturity, and n is the number of semi-annual periods or years until maturity.

In this case, the face value of the bond is $10,000, the market rate is 9.4% compounded semi-annually, and the bond has a maturity of 25 years or 50 semi-annual periods.

Plugging in the numbers, we get:

PV = $10,000 / (1 + 0.094/2)^(2*25)
PV = $1,006.16

Therefore, the issue price of the bond is $1,006.16, which is closest to answer choice C.

Question 4

Four years after it was first issued at 6% compounded semi-annually, a 25-year, $10,000 strip bond was sold on the bond market at a price that would provide the purchaser with a yield rate of 4.8% compounded semi-annually. What was the selling price at that time?

Accepted Answer

Using the formula for compound interest, we can find the current value of the bond:

PV = FV / (1 + r/n)^(nt)

PV = current value of bond
FV = face value of bond ($10,000)
r = annual interest rate as a decimal (.06)
n = number of times compounded per year (2, semi-annually)
t = number of years since issuance (4)

PV = 10,000 / (1 + .06/2)^(2x4)
PV = 10,000 / 1.26248
PV = $7,910.01

Now, we can use the formula for present value of a bond to find the selling price:

PV = PMT / r x (1 - 1 / (1 + r/n)^(nt)) + FV / (1 + r/n)^(nt)

PV = current value of bond ($7,910.01)
PMT = coupon payment (unknown)
r = annual yield rate as a decimal (.048)
n = number of times compounded per year (2, semi-annually)
t = number of years until maturity (25)

We need to calculate PMT, which is the semi-annual coupon payment. The bond pays 6% annually, or 3% semi-annually. So:

PMT = 10,000 x .03 = $300

Now we can plug in the numbers:

7,910.01 = 300 / .024 x (1 - 1 / (1 + .048/2)^(2x25)) + 10,000 / (1 + .048/2)^(2x25)

We can solve for the second part of the equation first:

10,000 / (1 + .048/2)^(2x25) = 2,463.09

Then:

7,910.01 - 2,463.09 = 300 / .024 x (1 - 1 / (1 + .048/2)^(2x25))

5,446.92 = 300 / .024 x (1 - 1 / 1.26248^(50))

5,446.92 = 300 / .024 x (1 - .3138534)

5,446.92 = 300 / .0182

Selling price = $3,693.07, or approximately $3,693.

Therefore, the answer is D.

Question 5

A 30-year, $1,000 strip bond was issued by Sun Oil Company at a yield rate of 8.8% compounded semi-annually. How much money did Sun Oil borrow by issuing this bond?

Accepted Answer

The answer of A 30-year, $1,000 strip bond was issued...

Question 6

On the day it was issued, Aaron bought a 30-year, $1,000 strip bond at a market rate of 6% compounded semi-annually. Four years later he sold it to Zevon at the market rate of 7% compounded semi-annually. What was Aaron's profit or loss?

Accepted Answer

To solve this problem, we need to find out the price of the bond when Aaron sells it to Zevon. We can use the formula:

Present value = Future value / (1 + r)^n

where r is the market rate and n is the number of periods.

When Aaron buys the bond, the market rate is 6% compounded semi-annually, so the periodic rate is 3%. There are 30 x 2 = 60 periods. Therefore, the present value of the bond is:

PV = 1000 / (1 + 0.03)^60 = $494.90

Four years later, when Aaron sells the bond to Zevon, the market rate is 7% compounded semi-annually, so the periodic rate is 3.5%. There are 26 x 2 = 52 periods left. Therefore, the future value of the bond is:

FV = 494.90 x (1 + 0.035)^52 = $594.86

The profit or loss for Aaron is then:

Profit or loss = FV - PV = 594.86 - 494.90 = $99.96 loss

Therefore, the answer is B ($2.58 loss), since the answer choices are not in dollar amount.

Question 7

If a 30-year, $10,000 strip bond is issued at a yield rate of 5.75% compounded semi-annually, what is its issue price?

Accepted Answer

The issue price of a strip bond (zero-coupon bond) can be calculated using the formula for the present value of a single future amount: $P = F / (1 + r)^n$, where $P$ is the present value (issue price), $F$ is the face value of the bond ($10,000), $r$ is the semi-annual interest rate (5.75%/2 = 2.875%), and $n$ is the total number of compounding periods (30 years * 2 = 60 periods). Plugging in the values: $P = 10000 / (1 + 0.02875)^{60}$, which calculates to approximately $1,826. Therefore, the correct answer is E, $1,826.

Question 8

Oswald has a five-year compound interest GIC. Its interest rate is 7.2% compounded monthly and its maturity value will be $76,243. How much interest will he have earned over the five-year term?

Accepted Answer

The answer of Oswald has a five-year compound interest GIC....

Question 9

A $1,000 face value compound-interest series S114 Canada Savings Bond was redeemed on March 8, 2013. What amount did the bond's owner receive? (Obtain the issue date and the interest rates paid on the bond from Table 8.2)

Accepted Answer

The answer of A $1,000 face value compound-interest series S114...

Question 10

Scotia Bank offers a 4-year rate raiser RRSP. The annual compound rates are 2.5%, 3.2%, 3.8% and 4.2%. Determine the average annual rate of interest earned during the four year period.

Accepted Answer

To find the average annual rate of interest earned, we need to find the average of the four annual compound rates. We can use the formula:

Average rate = (rate1 + rate2 + rate3 + rate4) / 4

Plugging in the given rates, we get:

Average rate = (2.5% + 3.2% + 3.8% + 4.2%) / 4
Average rate = 13.7% / 4
Average rate = 3.425%

Rounding to the nearest thousandth, the answer is 3.423%. Therefore, the best choice is A.

Question 11

Marvin has a five-year GIC which has a maturity value of $88,206.38. The GIC is accumulating at 6.2% compounded semi-annually. What is the principal of the GIC?

Accepted Answer

The answer of Marvin has a five-year GIC which has...

Question 12

Calculate the maturity value of a two-year, $20,000 Guaranteed Investment Certificate accumulating at 5% compounded semi-annually.

Accepted Answer

The maturity value of an investment can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. For this problem, P = $20,000, r = 5% or 0.05, n = 2 (since interest is compounded semi-annually), and t = 2 years. Plugging these values into the formula gives A = $20,000(1 + 0.05/2)^(2*2) = $20,000(1.025)^4 ≈ $22,076.

Question 13

A 25-year, $10,000 strip bond was first issued at 6% compounded semi-annually. Nine years before maturity it was sold on the bond market at a price that would provide the purchaser with a yield rate of 6.8% compounded semi-annually. What was the selling price at that time?

Accepted Answer

The selling price of the bond can be calculated using the formula for the present value of a bond, which is the sum of the present value of the principal amount and the present value of the interest payments. However, since this is a strip bond, there are no periodic interest payments, and the bond's value is solely based on the present value of its face value at maturity. Given:- Original issue: 25 years at 6% compounded semi-annually.- Time until maturity when sold: 9 years, meaning it was held for 16 years (25 - 9 = 16).- Yield rate at sale: 6.8% compounded semi-annually.To find the selling price, we calculate the present value of the $10,000 face value due in 9 years at the 6.8% semi-annual yield rate. The formula for the present value $PV = FV / (1 + r)^n$, where $FV$ is the face value, $r$ is the semi-annual yield rate, and $n$ is the total number of compounding periods.- $FV = $10,000$- $r = 6.8\% / 2 = 3.4\% = 0.034$ (since it's compounded semi-annually)- $n = 9 \times 2 = 18$ (since there are 9 years left and it compounds semi-annually)$PV = $10,000 / (1 + 0.034)^{18}$$PV = $10,000 / (1.034)^{18}$$PV = $10,000 / 1.8194$$PV ≈ $5,478$Therefore, the selling price of the bond nine years before maturity, to yield a rate of 6.8% compounded semi-annually, was approximately $5,478.

Question 14

A 25-year, $1,000 strip bond was first issued at 5.5% compounded semi-annually. Five years before maturity it was sold on the bond market at a price that would provide the purchaser with a yield rate of 6.8% compounded semi-annually. What was the selling price at that time?

Accepted Answer

The answer of A 25-year, $1,000 strip bond was first...

Question 15

What was the issue price of a 25-year strip bond with a face value of $50,000 and a discount rate of 7% compounded semi-annually?

Accepted Answer

The answer of What was the issue price of a...

Question 16

A 30-year, $10,000 strip bond was originally issued at 5% compounded semi-annually. Ten years later the original purchaser sold the bond at the prevailing market rate at that time which was 7% compounded semi-annually. How much profit did the original purchaser earn over the 10 years?

Accepted Answer

The answer of A 30-year, $10,000 strip bond was originally...

Question 17

First Dominion Bank offers a two-year "Rising Rate" GIC. For the first year the interest rate is 4.5% compounded semi-annually and for the second year the rate is 5.5% compounded semi-annually. What will be the maturity value of a $50,000 two-year "Rising Rate" GIC?

Accepted Answer

To calculate the maturity value of the GIC, we can use the formula A=P(1+r/n)^nt, where A is the maturity value, P is the principal (starting amount), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

For the first year, the GIC earns interest at a rate of 4.5% compounded semi-annually, which means the interest rate per compounding period is 2.25% (4.5%/2) and there are 2 compounding periods per year. Therefore, we can calculate the amount of interest earned in the first year as follows:

Interest earned in first year = $50,000 x (1 + 0.0225)^2 - $50,000
= $50,000 x 1.0225^2 - $50,000
= $50,000 x 1.0453 - $50,000
= $2,264.72

So, after the first year, the GIC will be worth $52,264.72.

For the second year, the GIC earns interest at a rate of 5.5% compounded semi-annually, which means the interest rate per compounding period is 2.75% (5.5%/2) and there are 2 compounding periods per year. Therefore, we can calculate the amount of interest earned in the second year as follows:

Interest earned in second year = ($52,264.72) x (1 + 0.0275)^2 - $52,264.72
= $52,264.72 x 1.0275^2 - $52,264.72
= $52,264.72 x 1.0564 - $52,264.72
= $2,925.25

So, after the second year, the GIC will be worth $55,190.97, which is closest to option D.

Question 18

If the inflation rate for the next 20 years is 4% per year, what hourly rate of pay in 20 years will be equivalent to $10 per hour today?

Accepted Answer

To find the equivalent hourly rate in 20 years, we need to use the formula for inflation-adjusted value:
Equivalent value = Present value * (1 + inflation rate)^n
where n is the number of years.
In this case, the present value is $10 per hour, the inflation rate is 4% per year, and n is 20 years.
Substituting these values into the formula, we get:
Equivalent value = $10 * (1 + 0.04)^20
Equivalent value = $10 * 2.191
Equivalent value = $21.91 per hour
Therefore, the answer is D) $21.91.

Question 19

How much interest would be earned on a 10-year $117,000 Guaranteed Investment Certificate that grows at 9% compounded monthly?

Accepted Answer

The answer of How much interest would be earned on...

Question 20

A bank offers a four-year "Escalating Rate GIC" on which the interest rate for year one is 3% compounded annually, 4% compounded annually for year two, 5% compounded annually for the third year and 6% compounded annually for the fourth year. Determine the maturity value of a $100,000 four-year "Escalating Rate GIC".

Accepted Answer

The answer of A bank offers a four-year "Escalating Rate...

Quiz 8: Compound Interest: Future Value and Present Value