Problem 1. The stock market has historically been a great investment. A reasonable estimate for the historical real annual stock market return is around 7%. Let us suppose that this rate of return is fixed.

(a) Use the \Rule of 72" to compute how many years it would take to double the initial amount. Compare with the exact number of years it would take to precisely double the initial amount.

When calculating how long will it take for an investment to double, a good approximation is to apply the rule of 72.

T ≈ 72100 r ≈ 72100 x 0,7 ≈ 10.29 years

The complete formula derives from the following expression:

P0 (1+r)t= 2P0
(1+r)t= 2 t ln (1+r) = ln (2) t= ln2ln(1+r)= ln2ln(1+0,07)=10.245 years

(b) How many years would it take for $10,000 to grow into $1 million dollars in real terms?
FV = PV (1+r)t
1,000,000 = 10,000 (1+0,07)t t ln (1+0,07) = ln (100) t= ln100ln(1+0,07)=68,06 years

Problem 2.

(a) Using the present value formula, explain why stocks are considered a good hedge against inflation.

In the long run, common stocks should prove a good hedge against inflation. Ideally, expenses, income and corporate earnings should behave at least as good as inflation and so should stock prices, usually these price changes can be transferred to the consumer. Second of all, stocks usually incorporate a “growth factor” which usually goes in agreement with economic trends. Economies grow, and what investors expect is that companies will grow too.

Using the present value formula, inflation has two components. A higher inflation should perpetuate a rise in expected future dividends as well as a rise in discount rates (r ) which account for higher inflation and a reduced purchasing power parity, therefore neutralizing the effect by making returns to be again lower. As interest rates decrease, people borrow money, spend more and