Respuesta :
The PV or Present Value of these payments is $843,533.
CALCULATION :-
The $100,000 immediate payment's present value (PV) is equal to $100,000.
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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