## nthenic_oftime one year ago 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?

1. misty1212

HI!!

2. nthenic_oftime

hey there how are you :) @misty1212

3. misty1212

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

4. misty1212

i am good you?

5. misty1212

for "semiannually" $$n=2$$ you get $\large 11,000(1+\frac{0.063}{2})^{2\times 10}$ or $\huge 11,000\left(1+\frac{.063}{2}\right)^{20}$

6. misty1212

got a calculator?

7. 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%?

8. 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

9. misty1212

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

10. misty1212

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

11. misty1212

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

12. nthenic_oftime

okay im following.

13. misty1212

now it is a calculator exercise

14. 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.

15. nthenic_oftime

medal for you :)

16. misty1212

$\color\magenta\heartsuit$