Set
9. Linzee's grandparents, on the day of her Quinceañera (15 th birthday) gave her \( \$ 20,000 \) (even though she missed a sectional basketball game). Linzee having learned about how important it is to start saving early is deciding on two investment options. Option 1 will pay her \( 4.05 \% \) interest compounded annually and Option \( B \) will pay her \( 4.01 \% \) compounded quarterly.
a. Write a function for Options 1 and 2 that calculate the value of the account after \( n \) years
(1) \( 20,000(1.0405)^{n}=x \)
(2) \( 20,000(1.0401 / 4)^{4 n}=x \).
b. Linzee plans leave the money in the account for 10 years and use it to pay for a trip around the world when she finishes college. Which option will yield more money and how much more?
\[
\begin{array}{ll}
20,000(1.0405)^{\circ}=x \rightarrow 29747.53 & \text { opTloN } 1 \\
20,000(1.0401 / 4)^{4(10)}=x \rightarrow 28260.58 & \text { by } ₫ 1486.95
\end{array}
\]
c. Algebraically determine, to the nearest tenth of a year, how long will it take for the better option to triple her money.