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Savings and Loans

Savings and Loans

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Author: Danny Whittaker
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Tutorial

Compound Interest

Our next exponential application is compound interest.  If you invest money at an annual interest rate your money will grow exponentially by the formula:

 

B equals P open parentheses 1 plus r over n close parentheses to the power of t asterisk times n end exponent

where B is the final Balance

P is the starting balance

r is the annual interest rate (don't forget to divide a percent by 100)

n is the number of times you earn interest each year

t is the number of years the money is invested

 

So, if you invest $100 at 8% annual interest compounded monthly for 50 years you will have:

B equals 100 open parentheses 1 plus fraction numerator.08 over denominator 12 end fraction close parentheses to the power of 12 asterisk times 50 end exponent equals $ 5387.82

We played around with different amounts of compounding and found that the more compoundings per year the more money you earn, but that the increase gets smaller and smaller with large values for n.

 

Explorations

Now that we've played with interest a bit, I want to know how long it will take to double an investment at different interest rates.  To simplify, take an initial investment of $100.  Working with a monthly compounding and with different interest rates, how long will it take to double the money to $200?  Work it out with at least five different interest rates.  See if you can come up with a rough rule for how long it will take for a different interest rate.