Question

Your eccentric (and rich uncle) is thrilled that you are pursuing your undergraduate in business administration. For the next 40 years (starting 1 year from now; last payment 40 years from now), he will pay you $2000 every odd year (1st, 3rd, etc.) and $3000 every even year (2nd, 4th, etc.). The relevant discount rate is 5% per year. What is the present value of all the money you will receive from this source over the next 40 years?

How to calculate with a financial calculator?

Answer 1

Question ask to calculate the present value of 40 year annuity in which you receive $2000 every odd year and $3000 every even year.

So there are 20 payments for each odd ad even years making total. We will calculate the Present value of two series separately and then combine the both.

1. PV of Series $3000 evert even year(2,4,.....20), makes 20 payments. So makes Series as $3000 every 2 years.

Periodic rate = 5 x 2 =10%

As per Requirement I am using Financial calculator texas ba 2.

Put Values in TVM as N=20, I/Y = 10, PMT = 3000, FV =0, Compute PV = 25540.69

PV of even Series = 25540.69

2. PV of Odd series of $2000. In this 1st Payment due after 1 year and next all after every 2 years. So we will first calculate the PV at End of year 1.

Get On BGN mode in calculator

Put values in TVM as = N=20, I/Y =10, PMT = 2000, FV=0, Compute PV= 18729.84

Now bring this PV 1 year back to time 0 as = 18729.84 / (1.05)

PV of Odd series = 17837.94

3. Combine both the PVs.

= 25540.69 + 17837.94

PV of the Annuity= 43378.63

However there 1 more possibility to calculate the answer is by using compound rate. If question specially told that 5% rate is Effective annual rate or annually compounding, then Periodic rate would be10.25% [(1.05)² -1]  intead of 10%. But question above write discount rate so expression of question here not seems to compund the rate.