1. ## Interest Problem

this is out of my chapter with exponential and logarithmic functions

Use the compound interest formulas
A=P(1 + r over n)^nt and A=Pe^rt

Suppose that you have $14,000 to invest. Which investment yields the greater return over 10 years: 7% compounded monthly or 6.85% compounded continuously? 2. Hello, kbryant05! Exactly where is your difficulty? . . You were sick for a week and missed all the lectures? . . You don't know how to use those formulas? . . You can't plug the stuff into your calculator? Use the compound interest formulas:$\displaystyle A\:=\:P\left(1 + \frac{r}{n}\right)^{nt}$and$\displaystyle A\:=\:Pe^{rt}$Suppose that you have$14,000 to invest.
Which investment yields the greater return over 10 years:
(a) 7% compounded monthly or (b)6.85% compounded continuously?
(a) 7% compounded monthly for 10 years.
We have: $\displaystyle P = 14,000,\;\;r = 7\% = 0.07,\;\;n = 12,\;\;t = 10$

Then: $\displaystyle A \;=\;14,000\left(1 + \frac{0.07}{12}\right)^{120} \;= \;28,135.25927\;\approx\;\$28,135.26$(b) 6.85% compounded continuously for 10 years. We have:$\displaystyle r = 6.85\% = 0.0685,\;\;t = 10$Then:$\displaystyle A\;=\;14,000e^{(0.0685)(10)}\;=\;27,772.8057\: \approx\;\$27,772.81$

Therefore, option (a) has the greater return.