Final answer:
The total future dollars of the investment at the end of 5 years is $155.68. The total interest generated from the investment is $47.36. The total future dollars and total dollar return from the investment in this certificate of deposit are $155.68 and $47.36, respectively.
Step-by-step explanation:
a. To calculate the total future dollars of the investment, we can use the formula for compound interest. The formula is given as:
P(1+r/n)ⁿt
Where:
P = Principal amount ($108.32)
r = Annual interest rate (7% or 0.07)
n = Number of times interest is compounded per year (2)
t = Number of years (5)
Substituting the values into the formula, we get:
Total future dollars = $108.32(1 + 0.07/2)⁽²ˣ⁵⁾
= $108.32(1 + 0.035)¹⁰
= $108.32(1.035)¹⁰
= $108.32(1.4332)
= $155.68
Therefore, the total future dollars of this investment at the end of 5 years is $155.68.
b. To calculate the total interest generated from the investment, we can subtract the principal amount from the total future dollars:
Total interest = Total future dollars - Principal amount
= $155.68 - $108.32
= $47.36
Therefore, the total interest generated from the investment in this certificate of deposit is $47.36.
c. Since the investor can purchase any investment for $108.32 that offers a 7% yield on a bond-equivalent basis and pays interest semiannually, the total future dollars and total dollar return from this investment will be the same as the calculation in part a and b, which is $155.68 and $47.36 respectively.
d. To calculate the total future dollars and total dollar return from the bond, we can use the same formula as in part a:
Total future dollars = $108.32(1 + 0.07/2)⁽²ˣ⁵⁾
= $108.32(1 + 0.035)¹⁰
= $108.32(1.035)¹⁰
= $108.32(1.4332)
= $155.68
After that, we can calculate the total dollar return by subtracting the initial price of the bond from the total future dollars:
Total dollar return = Total future dollars - Initial price
= $155.68 - $108.32
= $47.36
e. The coupon interest is the total amount of interest payments received over the life of the bond. In this case, it would be equal to the total interest calculated in part b, which is $47.36. There will be no capital gain or loss as the bond is held until maturity. The reinvestment income is the interest earned on the interest payments received. In this case, since the interest payments are semiannual, there will be 10 periods of reinvestment. The total dollar return is the sum of the coupon interest, capital gain/loss, and reinvestment income. Therefore, the values for each would be:
Coupon interest = $47.36
Capital gain/loss = $0
Reinvestment income = calculated based on interest payments and number of periods of reinvestment
Total dollar return = Coupon interest + Capital gain/loss + Reinvestment income
= $47.36 + $0 + Reinvestment income
f. To calculate the percentage of the total dollar return dependent on reinvestment income, we can divide the reinvestment income by the total dollar return and multiply by 100:
Percentage of total dollar return dependent on reinvestment income = (Reinvestment income/Total dollar return) × 100
= (Reinvestment income/$47.36) × 100
g. The reinvestment income in part e is the interest earned on the interest payments received. It is realized through the process of reinvesting the interest payments at the prevailing interest rate. The interest earned on the reinvested payments adds to the total dollar return of the investment.