Answer:
Option 1 PV lumpsum = $200000
Option2 PV of Annuity = $195413.08035 rounded off to $195413.08
Based on the present value of both the options, Option 1 should be chosen as it has a higher present value than option 2.
Explanation:
To decide on the best option to choose among the given two, we need to find the present value of both the options.
As the first option is to receive a lumpsum payment of $200000 today, the present value of this option is also equal to $200000 as it will be received today.
Option two, on the other hand, is an annuity as fixed payments will be received after equal intervals of time and for a limited time period and at the end of the period which satisfies the criteria of annuity ordinary. We will use the formula for the present value of annuity which is,
PV of Annuity = C * [( 1 - (1+r)^-n) / r]
Where,
- C is the periodic payment
- r is the rate of return of discount rate
- n is the number of periods
The periodic payment is provided as $1400. We are also provided with and APR of 6% which is the Annual rate. We will have to convert it into monthly rate by dividing it by 12. We are also provided with the number of years which we will need to convert into number of months by multiplying it by 12.
Monthly r = 6%/12 = 0.5%
Number of periods = 20 * 12 = 240
PV of Annuity = 1400 * [( 1 - (1+0.5%)^-240) / 0.5%]
PV of Annuity = $195413.08035 rounded off to $195413.08
