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What is the present value of receiving 10,000$ every other year for 20 years (you will...

What is the present value of receiving 10,000$ every other year for 20 years (you will receive 10 payments in total), if the annual interest rate (compounded annually) is 6%. The first payment is today.

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Expert Solution

- You wll receive $10,000 every other year for 20 years starting with the first payment today,i.e., $10,000 in every 2 years with total no of payments will be 10

First, we will convert annually Interest rate into 2-year effective annual Interest rate:-

2-year effective annual Interest rate = (1+r)^n - 1

Where,

r = Interest rate = 6%

n= no of periods = 2

2-year effective annual Interest rate = (1+0.06)^2 - 1

2-year effective annual Interest rate = 12.36%

Now, Since the Interest rate is also 2-year effective annual Interest rate and payments also incur every 2 years,

Calculating the Present Value of payments using PV of annuity due formula:-

Where, C= Periodic Payments = $10,000

r = Periodic Interest rate = 12.36%

n= no of periods = 10 payments

Present Value = $62,561.18

So, the present value is $62,561.18

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