Answer:
The first option, paying $2,000 per month for the next fifteen years (180 payments) with the first being made one month from now should be taken.
Explanation:
* Calculation of present value of the first option, paying $2,000 per month for the next fifteen years (180 payments) with the first being made one month from now:
We have: Discounting periods: 180; Discount rate = 6/12 = 0.5%; Monthly payment = 2,000
=> Present value = (2,000/0.5%) * [1 - 1.005^(-180)] = $237,007.3
* Calculation of present value of the second option, paying $785,000 twenty years from today.
We have: Effective rate = (1+0.5%)^12 - 1 = 6.168%
=> Present value = 785,000/(1+6.168%)^20 = $237,135.7
So, as the present value of option on is lower, it should be taken
Answer: $2000 per month for 15 years.
Explanation:
The first option is an annuity.
We can calculate it's present value by the following formula,
PV of an Annuity = P [ (1 – (1+i)^-n) / i ]
Where,
P is the cash flow per period
i is the rate of interest
n is the frequency of payments
The interest figure we are given needs to be converted to a monthly figure.
= 0.06/12 months
= 0.005
Plugging in the numbers we get
= 2000 ( 1- (1+0.005)^-180) / 0.005
= $237,007.03
This would be the present value of the first option you were given.
The second option would be to calculate the present value of $785,000 in 20 years, today.
That is a simple PV formula which is
= P/(1+r)^n
= 785,000/(1+0.06) ^20
= $244,766.71
Comparing the 2 present values shows that the first option is less than the second and so should be preferable.
Therefore paying $2000 a month for the next 15 years is better and should be taken.
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