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?

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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) About Me  (Show Source):
You can put this solution on YOUR website!

A=P%281%2Br%2Fn%29%5E%28n%2At%29 Start with the compound interest formula


25000=10000%281%2Br%2F2%29%5E%282%2A20%29 Plug in A=25000, P=10000, n=2 and t=20.


25000=10000%281%2Br%2F2%29%5E%2840%29 Multiply 2 and 20 to get 40.


25000%2F10000=%281%2Br%2F2%29%5E%2840%29 Divide both sides by 10000.


2.5=%281%2Br%2F2%29%5E%2840%29 Evaluate 25000%2F10000 to get 2.5.


root%2840%2C2.5%29=1%2Br%2F2 Take the 40th root of both sides.


1.02317165469772=1%2Br%2F2 Take the 40th root of 2.5 to get 1.02317165469772.


1.02317165469772-1=r%2F2 Subtract 1 from both sides.


0.0231716546977176=r%2F2 Combine like terms.


2%2A0.0231716546977176=r Multiply boths sides by 2 to isolate "r".


0.0463433093954353=r Multiply 2 and 0.0231716546977176 to get 0.0463433093954353.


r=0.0463433093954353 Rearrange the equation.


r=0.0463 Round to the nearest ten-thousandth.


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