Finance Calculation Help

Question

1. Suppose you invested $1000 to invest in two different compounding investment instruments that both earn 6% APR. But one has one compounding period per year and the other compounds monthly (i.e. 12 compound periods per year). .Calculate the total amount/balance in each instrument after 20 years. Which investment, if any, generates more money?
2. Suppose in a location with a “dry” climate, the probability of precipitation each day is 15%. However, it has been observed that a “rainy/snowy” day was preceded 60% of the time by “red” dawn. While red dawns began sunny days (i.e. no precipitation) 30% of the time. Using Bayes’ theorem, what is the probability of a rainy/snowy day if it started with a red dawn? How would this probability change if instead, the location was “wetter” where the daily probability of precipitation was 50% keeping the other probabilities constant?

Answer 1

Question 1. We need to look at monthly versus annual compounding.

With yearly we have 1000* (1+6%)²⁰ =3,207.13

with monthly we have 12 months per year for twenty years. Each month we earn 6%/12 or .0.5%. so we look at 1000*(1+i/12)^12*20years= 1000*(1.005)²⁴⁰ = 3,310.20

B )

I think the easiest way is to look at the "payoff matrix" if we have 1000 days we know that 15% or 150 days it rained. of those 150 days, 60% of the time there was a red dawn or. 6*150 = 90 days. Hence 60 of those rainy days there was no red dawn.

If it rains 150 days, 850 days it does not of those 850 days, 30% of the time there is a red dawn, or 255 days. so 595 days there is no red dawn.

No Rain Rainy Totals

Red Dawn 255 90 345

No Red 595 60 655

Totals 850 150 1000

so lets look at the first row. 255 days there are red dawns and 90 of those days it rains. so the P(rain|red dawn) = 90/255 =.3529

Why don't you try the same process for a rainy region (p(rain= .5)) or 500 out of 100 it rains.

Send it back to me

best, Lenny