Calculating Compounding Interest

[gemini070900]

Hi,

I'm struggling with this. Looking for some help: I have an investment that earns 10 % the 1st yr, 20 % the 2nd yr, and 30 % the 3rd year. Question: What rate of interest would earn the same rate of return after 3 yrs?

 

[mmm4444bot]

Hi Gemini:

You titled your post "Calculating Compounding Interest". Should we assume that the interest is compounded, with the 3-year fixed-rate investment? If so, then should we assume that the compounding period is once-per-year? Perhaps, the interest is continuously compounded.

Either way, you should start by picking a symbol to represent the principal, like P.

P = the principal

Now, using this symbolic principal, calculate what will be earned over the 3-year variable-rate investment, by writing down expressions for interest earned, added to the principal, and reinvested, year-by-year.

You can then use the result in the standard formula for compounded interest at rate r with period n after t years. The symbol P will divide out of that equation, and you'll be left with an equation to solve for r (the rate requested in your exercise).

If none of this rings any bells, please let me know. And clarify whether or not the fixed-rate investment has compounded interest (and, if so, the compounding period).

Otherwise, see if you can do the first step. Write an expression for how much you will have, if you invest P dollars for one year at 10% interest.

That expression becomes the new principal, in the 2nd year investment at 20%.

And so it goes.

 

[mmm4444bot]

Hi Gemini:

If you do not understand something that anybody here might tell you, then the appropriate response is to reply with specific questions.

Do not simply repost the exercise. You will end up having people trying to help you with the same exercise at more than one location on the boards (which is confusing and a waste of time).

If you invest P dollars at 10% simple interest, how many dollars do you have after 1 year?

The answer to this question is an expression containing the symbol P.

If you cannot figure out the answer to this question, then tell us. Otherwise, please show your work.

 

[galactus]

If x is the amount invested, then how much is there after 1 year at 10% interest?. x+.10x.

Then, the next year there is 20% interest: (x+.10x)+.2(x+.10x)

for 3 years: ((x+.10x)+.2(x+.10x))+.3((x+.10x)+(.2(x+.10x)))

Find the value of x and see what the increase is over the 3 years.

The formula for continuous interest is \(\displaystyle A=Pe^{rt}\)