a leasing contract calls for an immediate payment of $101,000 and nine subsequent $101,000 semiannual payments at six-month intervals. what is the pv of these payments if the annual discount rate is 9%?

The procedure for determining the present value of an ordinary annuity is used to determine the PV of the nine following $100,000 semiannual payments:

PV = P * [{1 - [1 / (1 + r)] ^n} / r] …………………………………. (1) (1)

Where;

PV is the present value of the nine more semi-annual payments of $100,000.
P = $100,000 in semi-annual payments

Effective semiannual interest, r, equals 8% divided by two, or 4%, or 0.04

n = 9 for the number of semi-annuals.

Equation (1) should be changed to reflect the values as follows:

PV = $100,000 * ((1 - (1 / (1 + 0.04))^9) / 0.04)

PV = $100,000 * ((1 - (1 / 1.04)^9} / 0.04)

PV = $100,000 * ((1 - 0.961538461538461^9) / 0.04)

PV = $100,000 * ((1 - 0.702586735578828) / 0.04)

PV = $100,000 * (0.297413264421172 / 0.04)

PV = $100,000 * 7.4353316105293

PV = $743,533

The PV of these payments is determined by:

The present value (PV) of the $100,000 immediate payment is added to the PV of these payments to arrive at $843,533 ($743,533 + $100,000).

The PV of these payments is therefore $843,533.

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