Interest Problem

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?

Quote:

Use the compound interest formulas: $A\:=\:P\left(1 + \frac{r}{n}\right)^{nt}$ and $A\:=\:Pe^{rt}$

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: $P = 14,000,\;\;r = 7\% = 0.07,\;\;n = 12,\;\;t = 10$

Then: $A \;=\;14,000\left(1 + \frac{0.07}{12}\right)^{120} \;= \;28,135.25927\;\approx\;\$28,135.26$

(b) 6.85% compounded continuously for 10 years.
We have: $r = 6.85\% = 0.0685,\;\;t = 10$

Then: $A\;=\;14,000e^{(0.0685)(10)}\;=\;27,772.8057\: \approx\;\$27,772.81$

Therefore, option (a) has the greater return.