Respuesta :
Answer:
The $641 to be received monthly for ten years is the option to be taken.
The reason is that the present value (PV), i.e. today’s value, of $641 to be received monthly for ten years is $56,451.91 and this is greater than a lump sum of $50,000 to be received today.
Explanation:
In order to decide on which option to take, the present value (PV) of $641 to be received monthly for ten years has to be calculated. This is done using the present value (PV) of an ordinary annuity formula as follows:
PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)
Where;
PV = Present value of all the monthly amount to receive = ?
P = Monthly amount to receive = $641
r = Interest rate = 6.5% annually = (6.5% ÷ 12) monthly = 0.541667% monthly or 0.00541667 montlhly
n = number of period = 10 years = 10 × 12 months = 120 months
Substituting the values into equation (1), we have:
PV = 641 × [{1 - [1 ÷ (1 + 0.00541666666666667)]^120} ÷ 0.00541666666666667]
= 641 × [{1 - [1 ÷ 1.00541666666666667]^120} ÷ 0.00541666666666667]
= 641 × [{1 - [0.994612515540821]^120} ÷ 0.00541666666666667]
= 641 × [{1 - 0.522962293183739} ÷ 0.00541666666666667]
= 641 × [0.477037706816261 ÷ 0.00541666666666667]
= 641 × 88.068499719925
PV = $56,451.91
The $641 to be received monthly for ten years is the option to be taken.
The reason is that the present value (PV), i.e. today’s value, of $641 to be received monthly for ten years is $56,451.91 and this is greater than a lump sum of $50,000 to be received today.
