exponential word problem

tsh44

Junior Member
Joined
Sep 4, 2005
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Hi I need some help with this problem.

The problem asks for the value of a $100 investment after 20years if the anuual interest rate is 10% and the interest is compounded monthly? and then continuously? What formulas would I use?
 
I got the compund interest for the monthly but I'm having trouble with the continuously.

The equation that was given to me was P = Ce^rt
I have gotten this far:

P= 100e^.10*20
P= 100e ^2

I don't know what to do next.
 
You are done if you can find e^2 on a calculator or table. You should have gotten 732.81 for the monthly. Continuous jumps it way up to 738.91
PS. Or you could get some paper and multiply 2.718282²
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Gene
 
Hi I need some help with this problem.

The problem asks for the value of a $100 investment after 20years if the anuual interest rate is 10% and the interest is compounded monthly? and then continuously? What formulas would I use?

With compound interest, the interest due and paid at the end of the interest compounding period is added to the initial starting principal to form a new principal, and this new principal becomes the amount on which the interest for the next interest period is based. The original principal is said to be compounded, and the difference between the the final total, the compound amount, accumulated at the end of the specified interest periods, and the original amount, is called the compound interest.
In its most basic use, if P is an amount deposited into an account paying a periodic interest, then S is the final compounded amount accumulated where S = P(1+i)^n, i is the periodic interest rate in decimal form = %Int./(100m), n is the number of interest bearing periods, and m is the number of interest paying periods per year. For example, the compound amount and the compound interest on $5000.00 resulting from the accumulation of interest at 6% annual interest compounded monthly for 10 years is as follows: Since m = 12, i = .06/12 = .005. Since we are dealing with a total of 10 years with 12 interest periods per year, n = 10 x 12 = 120. From this we get S = $5000(1+.005)^120 = $5000(1.8194) = $9097. Consequently, the compound interest realized is $9097 - $5000 = $4097. Of course the compound interest can be calculated directly from the simple expression I = P[(1+i)^n - 1].

This should enable you to solve your own problem.
 
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