By Proudhon Pierre-Joseph
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Extra info for Interest and Principal (letters)
If P0 is placed in an interest bearing account at an annual eﬀective rate of ieﬀ , if the annual inflation rate is iinf , and if the annual tax rate is t, then what is the after-tax after-inflation rate of interest? 13. A function f (x) on an interval I is said to be convex on I if for every p ∈ (0, 1) and every x, y ∈ I, the function f (x) satisfies5 f (px + (1 − p)y) ≤ pf (x) + (1 − p)f (y). (a) Show that the function f (x) = x is convex. (b) Show that the function f (x) = |x| is convex. (c) Show that the function f (x) = x2 is convex.
Assuming that each month has 30 days, what is the EFF? What is the IRR? 16. 8) on p. 36 to construct a table with the following headings, Annual Interest Rate Number of Years Rule Of for annual interest rates running from 1% to 30% in increments of 1%. The “Number of Years” column is the number of years it takes for the investment to double at the corresponding annual interest rate. The “Rule Of” column is calculated by multiplying the interest rate (as a percentage) by the number of years, as was the case in the Rule of 72.
Comment on this claim. 9. What is the IRR that corresponds to a simple interest investment rate of 20% over 5 years? Over 4 years? Over 10 years? 10. Hugh’s wife, Helen Kendrick, buys shares in Cisco for $68. Two months later they are worth $104. What is Helen’s IRR? 11. Hugh estimates that he needs $1,000,000 when he retires in 15 years. How much must he have in his current retirement account, which earns $8% a year compounded annually, to reach his goal assuming that he adds no more to his current account?
Interest and Principal (letters) by Proudhon Pierre-Joseph