SOLUTION: An investment of $10000 is guaranteed to have a return of $25000 in 20 years. If the interest is compounded semi-annually, what is the annual interest rate?

Question 676947: An investment of $10000 is guaranteed to have a return of $25000 in 20 years. If the interest is compounded semi-annually, what is the annual interest rate?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the compound interest formula

Plug in , , and .

Multiply and to get .

Divide both sides by .

Evaluate to get .

Take the 40th root of both sides.

Take the 40th root of to get .

Subtract 1 from both sides.

Combine like terms.

Multiply boths sides by to isolate "r".

Multiply and to get .

Rearrange the equation.

Round to the nearest ten-thousandth.

So the interest rate is 4.63% (multiply by 100 to convert to a percentage)

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