Macro-economics
- (a)The amount receivable today in a lump sum is equal to $1 million dollars less tax deductions i.e
Gross winning 1, 000,000
Less: Tax (400,000)
Nett lottery winning receivable today 600,000
(b) I would select the lump sum payment. This is because the money available at the present time is worth more than the same amount in the future due to its potential earning capacity according to the concept of the time value of money. It simply provides that as long as money available today can earn interest through investment, then it becomes worth when it received.
This is in line with the saying that “a bird in the hand is worth two in the push”.
This can be illustrated by finding the present value of the annuity payment of $ 100,000 for the 10 years and compared with the lump sum amount to determine which amount more than the other.
The present value of an annuity =Future value × Present value annuity factors (PVAL)
PVAF= 1-(1+0.05)^-10/0.05=4.3295
PV=FV×PVAFr%n years
PV=100,000×4.3295
=432950
Gross lottery winning =432950
Less: Tax at 40% (173180)
Net lottery winning 259,770
The net lottery winning receivable under the annuity option is $ 259,770.This amount is much less when compared with the lump sum of $600,000. Hence lump sum payment is the best option.
2(a)
Assumptions
A year has 365 nights
Years remaining to retirement = 65-22=43
Amount saved per year =5×365=1825
The total amount saved up to retirement year is the future value.
FV=PV{(1+r)^n-1)}/r = 182{(1+0.1)^43-1)}/0.1
= 1825×592.4007
=$1081131.26
=10,81131
(b) If the savings plan started later in life the time for savings would be shorter and hence the total amount that will accrue at the time of retirement will be lesser than when the saving started earlier like at 22 years.
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