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The compound interest formula is
where A is the amount earned, P is the principal, r is the annual interest rate, t is the time in years, and n is the number of compounding periods per year. Harry invested $5000 at 5% interest compounded quarterly (4 times per year). How much will the investment be worth after 5 years?
Answer: 18 years
Since you are trying to find when the compounded interest will turn 250 dollars into 500 dollars, you initial investment P = 250 and A = 500.
Since the annual interest rate is 4 percent, r = 0.04.
Since you are trying to find how long it will take for 250 dollars to increase to 500 dollars, you are looking for "n" in years.
Plug these values into the equation so that you get .
First, divide the 250 over so that you get
Next, take the log base 1.04 of both sides so that "n" will no longer be an exponent and you can solve for it.
Next, use the change of base formula:
where b = 1.04, a = 10, and x = 2
Put this in your calculator and you should get n = 17.673. However, since the interest is only compounded every year, it will take a full year to get at least 500 dollars. So, the answer is 18 years.
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