Algebra Math Question Help!

Question

Microsoft's stock price peaked at 6118% of its IPO price more than 13 years after the IPO† Suppose that $50,000 invested in Microsoft at its IPO price had been worth $3,000,000 (6000% of the IPO price) after exactly 13 years. What interest rate, compounded annually, does this represent? (Round your answer to two decimal places.)

Answer 1

If I is defined as the interest rate, then if P_o is the original principal or $50,000, P = 6*P_o = $3,000,000.

Compounding interest annually for 13 years means that each year, the principal increases to P*(1.00 + I).

That means after 13 years,

P = P_o * (1.00 + I)¹² = 6 * P_o Therefore,

(1.00 + I)¹² = 6  taking logarithms (base 10, although any base, including e, can be used) to simplify the calculations,

12 * log(1.00 + I) = log(6) = 0.77815

Log(1.00 + I) = 0. 77815/13 = 0.0648  Taking the exponential of each side,

1.0 + I = 10^0.0648 = 1.1609

I = 0.1609 = 16.09%