An investor places $30,000 into a stock fund. 10 years later the account has a v

Question

An investor places $30,000 into a stock fund. 10 years later the account has a value of $69,000. Using logarithms and anti-logarithms, present a formula for calculating the average annual growth rate for this fund.
Data Structures and Algorithm Analysis in C++ by Clifford Shaffer An investor places $30,000 into a stock fund. 10 years later the account has a value of $69,000. Using logarithms and anti-logarithms, present a formula for calculating the average annual growth rate for this fund.
Data Structures and Algorithm Analysis in C++ by Clifford Shaffer
Data Structures and Algorithm Analysis in C++ by Clifford Shaffer

Explanation / Answer

First we will derive formula....
If our initial amount = P1 and wirh r% interest rate, then end of year P2 - (1+r)P1.
As money will increased anually and amount increased with including compound interest,
then it will be like (1+r/n)^n.
We can also write as ==> lim(1+r/n)^n = e^r , where e is special character with 2.72 value.

So finally anually growth rate = p2/p1 = e^r

P2 = 69000 (given)
P1 = 30000 (given)
r = 10 years

If we apply log on both sides...
ln(p2-p1) = x (x is our growth rate)
==> ln(p2) - ln(p1)
==> 11.1418 - 10.89
===> 0.2518 ===> 25.18% growth rate

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.