In the first question, the problem is that the payment period (weekly) does not coincide with the interest period (monthly)
I will do an approximate solution by assuming 4 weeks per month, thus a monthly payment of $4000
Present value of option B = $600,00
present value of options A = 4000(1 - (1 + .03/12)^-600)/(.03/12)
= $1,243,322.84
clearly option A would be it
b) are they ever equal? let that time be n months
4000(1 - (1.0025)^-n)/.0025 = 600,000
1 - (1.0025)^-n = .375
1.0025^-n = .625
take logs etc
-n = log .625/log 1.0025 = -188.24
n = appr 188.24 months
I would answer it as 188 1/4 months or 188 months and 1 week
to have a true mathematical answer for b, we would have to convert the 3% per annum compounded monthly into a rate compounded weekly
let that weekly rate be j
then 1.0025^12 = (1+j)^52
(1+j)^52 = 1.0304159..
take the 52nd root
1+j = 1.0304159..^(1/52) = 1.000576369
so the weekly rate is .000576369
now repeat my calculation for b)
A lottery offers two options for the prize. Option A: $1000 a week for life. Option B: $600 000 in one lump sum
The current expected rate of return for large investment is 3%/a, compounded monthly.
a.Which option would the winner choose if s/he expects to live for another 50 years?
b. At what point in time is Option A better than Option B?
c. To answer (3b), did you assume that the winner would never spend any of that money? Write a brief reflection about which option you would choose, and why (pay attention to the math, but reflect upon how much money you would want to be spending as opposed to saving).
1 answer
5 answers