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?

Question

misty1212 · Answer

HI!!

nthenic_oftime · Answer

hey there how are you :) @misty1212

misty1212 · Answer

$6.25\%$ compounded continuously would give $$\large11,000\times e^{0.0625\times 10}$$ or 
$$\huge 11,000\times e^{0.625}$$

misty1212 · Answer

i am good
you?

misty1212 · Answer

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 · Answer

got a calculator?

nthenic_oftime · Answer

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 · Answer

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 · Answer

your rate was $6.25\%$ but you need to write it as a decimal first, so $6.25\%=0.0625$

misty1212 · Answer

and $p=11,000$ and also $t=10$ so we plug those in to the formula

misty1212 · Answer

that is where the $$\huge 11,000\times e^{0.625}$$ comes from

nthenic_oftime · Answer

okay im following.

misty1212 · Answer

now it is a calculator exercise

nthenic_oftime · Answer

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 · Answer

medal for you :)

misty1212 · Answer

$$\color\magenta\heartsuit$$