Rule 3: When there are two or more exponents to the same base, multiply them.
Problem 5: You have $1,000 in your account and will need $3,000 in ten years. You decide to invest your money in the following manner: You invest the $1,000 for three years at 12% compounded monthly. You then take the proceeds and invest them for one year at 11% compounded weekly. You then take the proceeds and invest them for two years at 10% compounded daily (360 days in a bank year). How much money would you have in the bank after the six years. How much interest will you need to get if you invest the proceeds for the last four years compounded annually.
Answer: At the end of six years, you will have $1,950.47. To have $3,000 in your bank after another four years you will need to get 11.3642% interest.
Solution:
This is a very simple problem if you use logarithms. If you
don't use logarithms, you will have to rely on trial and error.
Without logarithms:
The 12% guess is too high, so try a 11% rate as your second guess. If the rate is 11%, then
The 11% guess is too low. This means the actual rate is somewhere between 11% and 12%.
Try a 11.5% rate as your third guess. If you use 11.5% as
a rate, then
The 11.5% rate guess is too high. The real rate is somewhere between 11% and 11.5%.
Try a 11.25% rate as your fourth guess.
The 11.25% guess is too low. The actual rate is somewhere between 11.25% and 11.50%.
Try a rate of 11.37% as your fifth guess. If you use 11.37%
as a rate, then
This is close but still a little high.
Try a rate of 11.36% as your sixth guess. If you use 11.36%
as a rate, then
The 11.36% rate is close but a little low. The actual rate is between 11.36% and 11.37%.
You could keep on going in this manner until you obtained the
correct answer to accuracy that you required..
OR YOU COULD USE LOGARITHMS TO FIND THE INTEREST RATE
Divide both side of the equation
by $1,950.47 to have
Take the natural logarithm of both sides of the equation to get
By the rules of logarithms , this equation can be simplified to
or
This later expression can be written
x = .113642 or
If you want to learn more about how to use logarithms click on Logarithms
Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.
Author: Nancy Marcus