SOLUTION: If $7000 is invested at 8% compounded monthly, how much will this amount be at the end of 15 years? Use the formula, A = P (1 + r/n)^nt,where n is the number of times the investme
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Question 601674: If $7000 is invested at 8% compounded monthly, how much will this amount be at the end of 15 years? Use the formula, A = P (1 + r/n)^nt,where n is the number of times the investment is compounded per year. How long will it be until it is worth $12000?
I need one of the awesome tutor's to help me with this word problems, as I keep struggling trying to do the set up to solve. I get confused on how to know where to plug the values into the equation formula. Please help and explain step by step the reasoning behind the solution.
Thank you sooo much!!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Part 1)
If $7000 is invested at 8% compounded monthly, how much will this amount be at the end of 15 years?
Start with the compound interest formula
Plug in , (the decimal equivalent of 8%), (since we're compounding 12 times a year) and .
Evaluate to get
Add to to get
Multiply and to get .
Evaluate to get .
Multiply and to get .
Round to the nearest hundredth (ie to the nearest penny).
So at the end of 15 years, there will be $23,148.45 in the account.
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Part 2)
How long will it be until it is worth $12000?
Start with the compound interest formula
Plug in , , (the decimal equivalent of 8%), and .
Evaluate to get
Add to to get
Divide both sides by .
Evaluate to get .
Take the natural log of both sides.
Pull down the exponent using the identity .
Divide both sides by .
Evaluate the natural log of to get .
Evaluate the natural log of to get .
Divide.
Divide both sides by 12 to isolate "t".
Divide.
Rearrange the equation.
Round to the nearest whole number (ie to the nearest whole year).
So it will take about 7 years for the account to be worth $12,000
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