nthenic_oftime
  • nthenic_oftime
Use the compound interest formulas A = P (1+r/n) nt and A = Pert to solve. Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually?
Mathematics
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nthenic_oftime
  • nthenic_oftime
Use the compound interest formulas A = P (1+r/n) nt and A = Pert to solve. Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually?
Mathematics
katieb
  • katieb
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misty1212
  • misty1212
HI!!
nthenic_oftime
  • nthenic_oftime
hey there how are you :) @misty1212
misty1212
  • misty1212
\(6.25\%\) compounded continuously would give \[\large11,000\times e^{0.0625\times 10}\] or \[\huge 11,000\times e^{0.625}\]

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misty1212
  • misty1212
i am good you?
misty1212
  • misty1212
for "semiannually" \(n=2\) you get \[\large 11,000(1+\frac{0.063}{2})^{2\times 10}\] or \[\huge 11,000\left(1+\frac{.063}{2}\right)^{20}\]
misty1212
  • misty1212
got a calculator?
nthenic_oftime
  • nthenic_oftime
i sure do right here... could you explain a lil the first step you did sso i can do the same thing with 6.3%?
misty1212
  • misty1212
for the first one "continuously" you use the formula \[P\times e^{rt}\] where \(t\) is years and \(r\) is the rate of interest WRITTEN AS A DECIMAL
misty1212
  • misty1212
your rate was \(6.25\%\) but you need to write it as a decimal first, so \(6.25\%=0.0625\)
misty1212
  • misty1212
and \(p=11,000\) and also \(t=10\) so we plug those in to the formula
misty1212
  • misty1212
that is where the \[\huge 11,000\times e^{0.625}\] comes from
nthenic_oftime
  • nthenic_oftime
okay im following.
misty1212
  • misty1212
now it is a calculator exercise
nthenic_oftime
  • nthenic_oftime
so for 6.3% semiannually i got 20453.95 and 20550.70 for the 6.25% okay i got it thank you misty :) i appriciate it.
nthenic_oftime
  • nthenic_oftime
medal for you :)
misty1212
  • misty1212
\[\color\magenta\heartsuit\]

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