Question

What is the value today of a money machine that will pay $3,129.00 every six months for 13.00 years? Assume the first payment is made 3.00 years from today and the interest rate is 14.00%. Answer format: Currency: Round to: 2 decimal places.

Answer 1

Money Machine will pay every 6 months compencing first payment 3 years from today = $3129

Payment will be made for 13 years.

Calculating the Present Value of thse payment at the beginning of year 3 using Present Value of annuity due formula:-

Where, C= Periodic Annuity = $3129

r = Periodic Interest rate = 14%/2 = 7%

n= no of periods = 13 years*2 = 26

Present Value at year 3 is $39,593.06

Now, Calculating the Present value today from PV at year 3:-

Present Value today = Present Value at year 3/(1+r)^n

Where,

r = Periodic Interest rate = 14%/2 = 7%

n= no of periods = 3 years*2 = 6

Present Value today = $39,593.06/(1+0.07)^6

= $39,593.06/1.50073035185

= $26,382.53

So, value today of money machine is $26,382.53

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