Question 1

A bank quotes you a rate of 7% on a CD, compounded quarterly.What is the effective annual rate?
A)6.79%
B)6.81%
C)6.87%
D)7.13%
E)7.19%

Accepted Answer

The effective annual rate (EAR) can be calculated using the formula: EAR = (1 + i/n)^(n*t) - 1, where i is the nominal interest rate, n is the number of compounding periods per year, and t is the time in years. Plugging in the given values: EAR = (1 + 0.07/4)^(4*1) - 1 = 1.071857 - 1 = 0.071857 or 7.19%.

Question 2

If you invested $200 today, another $400 in one year, and another $600 in two years, how much will your investment be worth (to the nearest dollar) in five years, assuming a 7% annual compound return?
A)$1,540
B)$600
C)$720
D)$770
E)None of the above

Accepted Answer

To calculate the future value of the investment after 5 years, we need to apply the compound interest formula:

FV = PV * (1 + r)^n

Where FV is the future value, PV is the present value, r is the annual interest rate as a decimal, and n is the number of years.

Using this formula for each investment separately:

- The first investment of $200 today will be worth $200 * (1 + 0.07)^5 = $295.03 in five years.

- The second investment of $400 in one year will be worth $400 * (1 + 0.07)^4 = $532.90 in five years.

- The third investment of $600 in two years will be worth $600 * (1 + 0.07)^3 = $776.16 in five years.

Adding up the future values of the three investments, we get:

FV = $295.03 + $532.90 + $776.16 = $1,604.09

Rounding to the nearest dollar, the answer is $1,540. Therefore, the correct answer is A.

Question 3

If a bond is selling at a premium, then:
A)the yield to maturity is less than the coupon rate.
B)the yield to maturity is greater than the coupon rate.
C)the yield to maturity is equal to the coupon rate.
D)its duration must be greater than its maturity.
E)its duration must be equal to its maturity.

Accepted Answer

When a bond is selling at a premium, it means that its market price is higher than its par value. This happens when the coupon rate of the bond is higher than the prevailing interest rates in the market. As a result, investors are willing to pay more for the bond to receive higher interest payments. This also implies that the yield to maturity (the total return an investor can expect from the bond if held until maturity) is less than the coupon rate.

Question 4

To the nearest dollar, what is the value today of an investment that pays $15,000 in seven years, assuming an annual opportunity cost of 9%?
A)$7,473
B)$27,421
C)$8,206
D)$7,130
E)None of the above

Accepted Answer

To calculate the present value of the investment, we can use the formula: PV = FV / (1 + r)^(n), where PV is the present value, FV is the future value, r is the annual opportunity cost, and n is the number of years.

Plugging in the values, we get:
PV = 15,000 / (1 + 0.09)^7
PV = 15,000 / 1.9487
PV = 7,698.47

Rounding to the nearest dollar, we get:
PV = $8,206
Therefore, the answer is choice C.

Question 5

What is the effective annual rate of an investment that offers 8%, compounded quarterly?
A)8.00%
B)8.16%
C)8.24%
D)8.32%
E)8.64%

Accepted Answer

The formula to calculate effective annual rate (EAR) with quarterly compounding is:

EAR = (1 + i/n)^n - 1

where i is the nominal annual interest rate (8%) and n is the number of compounding periods per year (4 for quarterly).

EAR = (1 + 0.08/4)^4 - 1 
EAR = 0.0824 or 8.24%

Therefore, the effective annual rate of the investment is 8.24%. The best choice is (C).

Question 6

What is the effective annual cost of a credit card that charges 18%, compounded monthly?
A)16.63%
B)18.00%
C)18.81%
D)19.56%
E)19.61%

Accepted Answer

The answer of What is the effective annual cost of...

Question 7

In January, you purchased a 14% semi-annual coupon bond ($1,0000 par) that had a remaining maturity of five years for $827.95.Six months later, immediately following an interest payment, you sold the bond.At the time of the sale, interest rates were 10%.What was your return?
A)7.1%
B)38.2%
C)46.4%
D)146.4%
E)296.3%

Accepted Answer

First, we need to calculate how much the bond was worth six months later after receiving the coupon payment:
Coupon payment = 14%/2 * $1,000 = $70
Remaining principal = $1,000
PV factor for 2.5 years at 10% = 0.62092 (from a financial calculator)
Value of the bond = $70 / (1 + 10%/2) + $1,000 / (1 + 10%/2)^5 = $1,038.80
We can then calculate the return:
Sale price = $1,038.80
Purchase price = $827.95
Coupon payments received = $70 (received once)
Total return = ($1,038.80 - $827.95 + $70) / $827.95 = 0.464 or 46.4%

Question 8

If you invested $700 today and another $1,000 in two years, to the nearest dollar, how much will your investment be worth in seven years.? Assume an 8.4% annual compound return.
A)$616
B)$749
C)$1,364
D)$2,728
E)None of the above

Accepted Answer

The $700 investment will grow for 7 years, and the $1,000 investment will grow for 5 years. Using the compound interest formula: Future Value = Present Value * (1 + rate)^n, the total future value is $700*(1.084)^7 + $1,000*(1.084)^5 = $1,228.44 + $1,499.56 = $2,728.

Question 9

A bond with a par value of $1,000 and a 13% semi-annual coupon rate has 20 years to maturity.Assuming it is priced to yield 10%, compounded semi-annually, what is the market value of the bond, to the nearest dollar?
A)$1,187
B)$1,107
C)$1,257
D)$2,373
E)None of the above

Accepted Answer

The market value of the bond can be calculated using the present value of its future cash flows, which include the semi-annual coupon payments and the par value at maturity. The bond pays $65 every six months (13% of $1,000 divided by 2), and the yield is 5% per period (10% annual yield divided by 2). Using the present value formula for an annuity and a lump sum, the market value is approximately $1,257.

Question 10

To the nearest dollar, what is the value today of an investment that pays $10,000 in five years, assuming an annual opportunity cost of 6%?
A)$7,473
B)$11,592
C)$8,626
D)$7,130
E)None of the above

Accepted Answer

To find the present value of an investment, you use the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the annual interest rate, and n is the number of years. Plugging in the given values: PV = $10,000 / (1 + 0.06)^5 = $7,472.58, which rounds to $7,473.

Question 11

A bond with a par value of $1,000 and a 10% semi-annual coupon rate has 9 years to maturity.Assuming it is priced to yield 8%, compounded semi-annually, what is the market price of the bond, to the nearest dollar?
A)$1,074
B)$1,127
C)$1,450
D)$1,510
E)None of the above

Accepted Answer

The answer of A bond with a par value of...

Question 12

If a bond is selling at a discount, then:
A)the yield to maturity is less than the coupon rate.
B)the yield to maturity is greater than the coupon rate.
C)the yield to maturity is equal to the coupon rate.
D)its duration must be greater than its maturity.
E)its duration must be equal to its maturity.

Accepted Answer

When a bond is selling at a discount, it means its market price is lower than its face value or par value. This implies that the yield to maturity is greater than the coupon rate, as the investor is purchasing the bond at a lower price but will receive the full par value at maturity.

Question 13

You invested $10,000 ten years ago.During the first two years, you earned 9% per year and during the last eight years, you earned 12% per year.To the nearest dollar, how much is your investment worth today?
A)$25,937
B)$29,417
C)$37,014
D)$40,456
E)None of the above

Accepted Answer

The answer of You invested $10,000 ten years ago.During the...

Question 14

A bank quotes you an effective annual rate of 10% on a semi-annual investment.What is the annual simple interest rate?
A)9.76%
B)10.00%
C)10.25%
D)10.79%
E)10.96%

Accepted Answer

The effective annual rate is given by:
(1+periodic rate)^n - 1
where n is the number of periods in a year and periodic rate is the interest rate per period.
In this case, the effective annual rate is 10%, which means:
(1+periodic rate)^2 - 1 = 0.1
Simplifying this equation yields:
periodic rate = 0.048 or 4.8%
The annual simple interest rate is just twice the periodic rate, or:
2 * 4.8% = 9.76%. Therefore, the answer is choice A.

Question 15

At what annual interest rate will you double your money if you invest for 8 years?
A)10.11%
B)9.05%
C)8.19%
D)7.91%
E)6.73%

Accepted Answer

The answer of At what annual interest rate will you...

Question 16

Assuming an 8% return, compounded semi-annually, what is the market value of a 12% coupon bond with three years to maturity?
A)$1,000.00
B)$1,104.84
C)$1,419.68
D)$1,809.35
E)$2,000.00

Accepted Answer

The bond has a 12% coupon rate, which means it pays $120 per year ($1,000 x 12%). The bond has three years to maturity, so it will make six semi-annual payments ($120/2 = $60 per payment). Using the formula for the present value of a bond, the market value is:
MV = ($60 / (1 + (0.08/2))^1) + ($60 / (1 + (0.08/2))^2) + ($60 / (1 + (0.08/2))^3) + ($60 / (1 + (0.08/2))^4) + ($60 / (1 + (0.08/2))^5) + ($1,060 / (1 + (0.08/2))^6)
MV = $1,104.84 (rounded to the nearest penny)

Question 17

To the nearest dollar, what is the value today of an investment that pays $1,000,000 in 15 years, assuming an annual opportunity cost of 8%?
A)$555,265
B)$315,242
C)$463,193
D)$3,238,387
E)None of the above

Accepted Answer

The answer of To the nearest dollar, what is the...

Question 18

You purchase a 10-year bond at face value for $1,000.It pays a semi-annual coupon payment of $50.If you can reinvest the coupon payments at 8% annually, what is your expected total return?
A)5.73%
B)6.63%
C)7.53%
D)8.43%
E)9.33%

Accepted Answer

The answer of You purchase a 10-year bond at face...

Question 19

How long will it take you to double your money if you can invest at 7.2% per year?
A)9.97 years
B)9.28 years
C)8.62 years
D)7.21 years
E)6.98 years

Accepted Answer

The Rule of 72 is a simple way to estimate the number of years required to double the investment at a fixed annual rate of interest. By dividing 72 by the annual interest rate, you get the approximate number of years. For a 7.2% interest rate, 72 / 7.2 = 10 years. However, the closest option is 9.97 years, which accounts for more precise calculations.

Question 20

If a bond is selling at par value, then:
A)the yield to maturity is less than the coupon rate.
B)the yield to maturity is greater than the coupon rate.
C)the yield to maturity is equal to the coupon rate.
D)its duration must be greater than its maturity.
E)its duration must be equal to its maturity.

Accepted Answer

When a bond is selling at par value, it means that the market interest rate is such that the yield to maturity (YTM) equals the coupon rate. Therefore, the answer is (C). Neither the duration nor the maturity affect the relationship between the YTM and coupon rate when a bond is selling at par value, so options (D) and (E) are not correct.

Quiz 6: Pricing Fixed-Income Securities

A bank quotes you a rate of 7% on a CD, compounded quarterly.What is the effective annual rate?

If you invested $200 today, another $400 in one year, and another $600 in two years, how much will your investment be worth (to the nearest dollar) in five years, assuming a 7% annual compound return?

If a bond is selling at a premium, then:

To the nearest dollar, what is the value today of an investment that pays $15,000 in seven years, assuming an annual opportunity cost of 9%?

What is the effective annual rate of an investment that offers 8%, compounded quarterly?

What is the effective annual cost of a credit card that charges 18%, compounded monthly?

In January, you purchased a 14% semi-annual coupon bond ($1,0000 par) that had a remaining maturity of five years for $827.95.Six months later, immediately following an interest payment, you sold the bond.At the time of the sale, interest rates were 10%.What was your return?

If you invested $700 today and another $1,000 in two years, to the nearest dollar, how much will your investment be worth in seven years.? Assume an 8.4% annual compound return.

A bond with a par value of $1,000 and a 13% semi-annual coupon rate has 20 years to maturity.Assuming it is priced to yield 10%, compounded semi-annually, what is the market value of the bond, to the nearest dollar?

To the nearest dollar, what is the value today of an investment that pays $10,000 in five years, assuming an annual opportunity cost of 6%?

A bond with a par value of $1,000 and a 10% semi-annual coupon rate has 9 years to maturity.Assuming it is priced to yield 8%, compounded semi-annually, what is the market price of the bond, to the nearest dollar?

If a bond is selling at a discount, then:

You invested $10,000 ten years ago.During the first two years, you earned 9% per year and during the last eight years, you earned 12% per year.To the nearest dollar, how much is your investment worth today?

A bank quotes you an effective annual rate of 10% on a semi-annual investment.What is the annual simple interest rate?

At what annual interest rate will you double your money if you invest for 8 years?

Assuming an 8% return, compounded semi-annually, what is the market value of a 12% coupon bond with three years to maturity?

To the nearest dollar, what is the value today of an investment that pays $1,000,000 in 15 years, assuming an annual opportunity cost of 8%?

You purchase a 10-year bond at face value for $1,000.It pays a semi-annual coupon payment of $50.If you can reinvest the coupon payments at 8% annually, what is your expected total return?

How long will it take you to double your money if you can invest at 7.2% per year?

If a bond is selling at par value, then: