Question

We buy a 6% bond for $850 and sell it in 3 years for $950. We

invest the $30 we receive every 6 months at 5% semiannual rate.
Compute the annual rate of your investment.

Answer 1

The annual rate of return on your investment is approximately 8.98%.

To calculate the annual rate of return on your investment, follow these steps:

1. Calculate the total return on the bond investment:

- Purchase Price = $850

- Selling Price = $950

- Semiannual Coupon Payment = 6% * $850 / 2 = $25 (since it's a 6% bond with semiannual payments)

Total Return = Selling Price + Total Coupon Payments - Purchase Price

Total Coupon Payments = 2 * $25 every 6 months for 3 years = 6 * $25 = $150

Total Return = $950 + $150 - $850 = $250

2. Calculate the future value (FV) of the reinvested coupon payments:

- Coupon Payment = $25 every 6 months

- Semiannual Interest Rate = 5%

- Number of Periods = 2 times per year for 3 years = 6 periods

FV = Coupon Payment * [(1 + Semiannual Interest Rate)^Number of Periods - 1] / Semiannual Interest Rate

FV = $25 * [(1 + 0.05)^6 - 1] / 0.05 ≈ $163.97

3. Calculate the total future value:

Total Future Value = FV + Selling Price = $163.97 + $950 ≈ $1,113.97

4. Calculate the annual rate of return using the formula for compound interest:

`\[Total Future Value = Principal * (1 + Annual Rate)^Number of Years\]`

Rearrange the formula to solve for the annual rate:

`\[Annual Rate = (Total Future Value / Principal)^(1 / Number of Years) - 1\]`

Annual Rate = ($1,113.97 / $850)^(1 / 3) - 1 ≈ 0.0898 or 8.98%

So, the annual rate of return on your investment is approximately 8.98%.