What is the total present value of 80 received in one year 300 received in two years and 700 received in six years if the discount rate is 7?

Answer 1

$3304.85The basic problem can be broken down like this:

• First find the PV of the sum of $80 that is received in year 1. Using interest factor (1yr @7%) tables found in most finance text books that will be $74.80 ($80*0.935)
• Next you need to find the PV of annuity for two years of $300 @7%. Using interest factors this will be $542.20 ($300*1.808). But this is the PV at year 1 since the payments started in Year 2. Now you need to convert this PV to year 0 by using the interest factor for a sum for one year and multiplying $542.20 by this factor (0.935). This will give a result of $507.14
• Finally you need to find the PV of annuity for six years of $700 @7%. Using the interest factors this will be $3336.90 ($700*4.767). But this is the PV at year 3, so you will need to convert this to PV @ year 0 buy multiplying this # by the interest factor for the PV of a sum for 3 yrs @7% (0.816) to get $2722.91
• Now you add the three results together to get the present value @ year 0: $74.80 + $507.14 + $2722.91 to get the answer of $3304.85