Question 1

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

The answer of Four years after it was first issued...

Question 2

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

The average annual rate of interest is calculated by adding the annual rates together and dividing by the number of years. So, (2.5% + 3.2% + 3.8% + 4.2%) / 4 = 13.7% / 4 = 3.425%. The closest option to this calculation is 3.423%.

Question 3

Today, in Brazil, there are 462,966 people in prison. The prison population there has been decreasing at a rate of 1.9% per year for the last 10 years. How many prisoners were there in Brazil 10 years ago?

Accepted Answer

To find the number of prisoners 10 years ago, we can use the formula for exponential growth/decay: $P = P_0(1 + r)^t$, where $P$ is the final amount, $P_0$ is the initial amount, $r$ is the rate (as a decimal), and $t$ is the time in years. Rearranging to solve for $P_0$, we get $P_0 = \frac{P}{(1 + r)^t}$. Substituting $P = 462,966$, $r = -0.019$ (since the population is decreasing), and $t = 10$, we find $P_0 = \frac{462,966}{(1 - 0.019)^{10}}$, which calculates to approximately 560,866.

Question 4

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 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

The number of people working in service industries in British Columbia has been growing at a rate of 4% per year for eight years. Today there are 1.86 million service workers in B.C. How many were there five years ago?

Accepted Answer

The answer of The number of people working in service...

Question 7

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 8

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 9

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 10

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

Aaron's profit or loss is calculated by finding the present value of the bond when he bought it and when he sold it. Initially, the bond's present value is calculated using a 6% semi-annual rate for 60 periods (30 years), and when sold, using a 7% semi-annual rate for 52 periods (26 years remaining). The difference in these values results in a loss of $2.58.

Question 11

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

The answer of If the inflation rate for the next...

Question 12

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-year...

Question 13

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

The answer of A 25-year, $10,000 strip bond was issued...

Question 14

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 15

The population of Ourtown, Saskatchewan is expected to grow at a rate of 2.5% per year for the next five years. If the current population is 11,763 what is it expected to be in five years?

Accepted Answer

The population in five years can be calculated using the formula for compound growth: P = P0(1 + r)^t, where P0 is the initial population, r is the growth rate per period, and t is the number of periods. Substituting the given values: P = 11763(1 + 0.025)^5 ≈ 13309.

Question 16

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 17

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 correct answer is A because the issue price of a strip bond is equal to the present value of its future cash flows. In this case, the future cash flows are the semi-annual interest payments of $1,750 and the face value of $50,000 at maturity. Using the formula for the present value of an annuity, we can calculate the issue price as follows:PV = PMT * [1 - (1 + r)^-n] / rwhere:PV is the present valuePMT is the semi-annual interest paymentr is the semi-annual discount raten is the number of semi-annual periodsPlugging in the values, we get:PV = $1,750 * [1 - (1 + 0.07/2)^-(25*2)] / (0.07/2)= $1,750 * [1 - (1.035)^-50] / 0.035= $1,750 * 18.424= $32,242Therefore, the issue price of the strip bond is $32,242.

Question 18

Bones McGoo weighs 218 kilograms. His goal is to decrease his weight by 5% each year for 15 years. What will he weigh in 15 years if he achieves his goal?

Accepted Answer

Bones McGoo will weigh 101 kg in 15 years if he achieves his goal of decreasing his weight by 5% each year.To calculate his weight in 15 years, we can use the formula:Weight in 15 years = Initial weight * (1 - 5%)^15Weight in 15 years = 218 kg * (1 - 0.05)^15Weight in 15 years = 218 kg * 0.463Weight in 15 years = 101 kg

Question 19

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 selling price is calculated using the present value formula for bonds. The bond has 5 years remaining, with a yield rate of 6.8% compounded semi-annually. The present value of the bond is calculated as $1,000 / (1 + 0.034)^10, which equals approximately $716.

Question 20

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.

Quiz 8: Compound Interest: Future Value and Present Value