SOLUTION: How much money should Sheila invest in an account that earns 8% annual interest compounded monthly in order to have $4,000 in 5 years?
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Question 312093: How much money should Sheila invest in an account that earns 8% annual interest compounded monthly in order to have $4,000 in 5 years?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
^{nt})
Is the Future Amount, 
, of an investment of 
at an annual rate of 
compounded 
times per year for 
years.
You want to know so that 
when 
, 
, and 
Substitute the values and do whatever arithmetic is readily apparent:
^{60})
Multiply through by ^{60}})
^{60}})
Take the log of both sides (any base, doesn't matter):
\ =\ \ln\left(\frac{4000}{(1.00\overline{6})^{60}}\right))
Apply the logarithm rules:
\ =\ \ln(4000)\ -\ \ln\left((1.00\overline{6})^{60}\right))
\ =\ \ln(4000)\ -\ 60\,\cdot\,\ln\left(1.00\overline{6}\right))
Which is to say:
\ -\ 60\,\cdot\,\ln\left(1.00\overline{6}\right)})
Then a little calculator work:
John
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