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Question regarding present value with discount rate

Personal Finance & Money Asked on February 20, 2021

I am a novice at finance subjects and need to find out Present value given a few details

The university fees of $45,000 a year will have be paid starting 11 years from today. He is analysing an insurance plan that pays out $45,000 a year for 4 years with the first payout 11 years from today. The insurance plan has several payment options:

Option 1
Pay $60,000 today

Option 2
Beginning 1 year from today, pay $12,000 a year for the next 8 years

Option 3
Beginning 1 year from today, make payments each year for the next 8 years. The first payment is $11,000 and the amount increases by 5% each year

The question is asking to calculate Present Value for each option with a 10% discount rate.

I understand that PV = FV / (1 + r)^t

Am I right to say that FV is $180,000, r is 0.1 and t is 11 years?
And if so, Option 1 PV = $180000 / 1.1^11 = $63088.90

But I am stucked for Option 2 and 3, how do I move on from here?

One Answer

Your answer for the PV of the insurance is not right. You need to discount each of the 4 payments separately since they occur at different times. So the total PV would be

  45,000 / (1.1)^11  
+ 45,000 / (1.1)^12 
+ 45,000 / (1.1)^13 
+ 45,000 / (1.1)^14
--------------------
  54,995

For 2 and 3, find the PV of each option and compare it to the PV of the insurance plan. You'll need to calculate the PV of each cash flow separately. So the answer to #2 would be

  12,000 / (1.1)^1  
+ 12,000 / (1.1)^2 
+ 12,000 / (1.1)^3 
...

and 3 would be

  11,000            / (1.1)^1  
+ 11,000 * (1.05)^1 / (1.1)^2 
+ 11,000 * (1.05)^2 / (1.1)^3 
...

Correct answer by D Stanley on February 20, 2021

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