Slick Sam has a special relationship with his banker. The nature of the relationship is as follows: The bank owes Sam $100 per year forever. The 1st payment is due in 1 year. The bank will borrow or lend money to Sam at a constant effective rate of i per year. Today, Sam calculated the present value of the payments that are due to him as X. Sam can receive his first 16 payments at the end of year 16 in a lump sum. If he does that, then the total value of the lump sum and future payments at the end of the sixteenth year is X + 2,000. Calculate X.

X=97.24

Explanation:

PV = Present Value = X+2000 by the 16th years

PMT = Payments = $100

FV = Future Value = 2000 at the end of 16 years

n= number of years

Applying the equation of future value for annuity

FV = pmt* ((1+r)ⁿ - 1   )/r

Inputting the values;

2000=100*((1+r)¹⁶-1)/r

Solving for r, gives r = 2.9%

Therefore using the formula for PV for annuity;

PV=PMT*(1-(1/1+r)/r)

X=100*(1-(1/1.029)/0.029

X=100*((1-0.9718)/0.029)

X=100*(0.0282/0.029)

X=97.24

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