# exponential word problem

• Dec 9th 2008, 02:24 PM
ferken
exponential word problem
Hi I have no idea where to start for this problem.
Much help is needed, thanks in advance.

In 1930, the bluenose stamp could be bought for 50 cents. In 1987, the same stamp was sold at an auction for 500 dollars. What annual rate of interest corresponds to an investment of 50 cents in 1930 which grew to 500 dollars in 1987
• Dec 9th 2008, 03:00 PM
Soroban
Hello, ferken!

Quote:

In 1930, the bluenose stamp could be bought for 50 cents.
In 1987, the same stamp was sold at an auction for 500 dollars.
What annual rate of interest corresponds to an investment of 50 cents in 1930
which grew to 500 dollars in 1987

This is a compound interest problem.

Formula: .$\displaystyle A \;=\;P(1+r)^n$ . where: .$\displaystyle \begin{Bmatrix}P &=& \text{Principal invested} \\ r &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \\ A &=& \text{Final value} \end{Bmatrix}$

We have: .$\displaystyle P = \$0.50,\;A = \$500,\;n = 57$

The formula becomes: .$\displaystyle 0.50(1 + r)^{57} \:=\:500 \quad\Rightarrow\quad (1 + r)^{57} \:=\:1000$

. . $\displaystyle 1 + r \:=\:1000^{\frac{1}{57}} \;=\;1.128837892 \quad\Rightarrow\quad r \:=\:0.128837892$

Therefore: .$\displaystyle r \;\approx\;12.9\%$