Question

An investment promises the following payments: March 12 $1000; March 18 $2000; March 26 $3000 If the market interest rate is 10.8%, what is this investment value on March 18? What is the investment value on March 1? What is the investment value on March 30?

Answer 1

1.
`\( PV_{\text{March 18}} \approx (2000)/((1 + 0.108)^(0.6)) \)`

2.
`\( PV_{\text{March 1}} \approx (1000)/((1 + 0.108)^(0.0333)) \)`

3.
`\( PV_{\text{March 30}} = (3000)/((1 + 0.108)^(1)) \)`

To calculate the present value of future cash flows, you can use the formula:
`\[ PV = (FV)/((1 + r)^n) \]`

Where:

- \( PV \) is the present value,

- \( FV \) is the future value (cash flow),

- \( r \) is the interest rate per period,

- \( n \) is the number of periods.

Let's calculate the present values for each date:

1. March 18:
`\[ PV_{\text{March 18}} = \frac{2000}{(1 + 0.108)^{(18)/(30)}} \]`

2. March 1:
`\[ PV_{\text{March 1}} = \frac{1000}{(1 + 0.108)^{(1)/(30)}} \]`

3. March 30:
`\[ PV_{\text{March 30}} = \frac{3000}{(1 + 0.108)^{(30)/(30)}} \]`

Now, calculate the values:

1.
`\( PV_{\text{March 18}} \)`

2.
`\( PV_{\text{March 1}} \)`

3.
`\( PV_{\text{March 30}} \)`

Please note that the time is expressed in years, and the number of days is relative to a 30-day month.