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) $20, 000 = (1.0405)^{n}$
(2) $20, 000 = (1.0401 / 4)^{4 n}$
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?

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Answer

Option 1 will yield more money, the difference is approximately $29714.47 - 29713.14 \approx $ 1.33$

Steps

Step 1 ： $A_{1} (n) = 20000 (1.0405)^{n}$

Step 2 ： $A_{2} (n) = 20000 (1 + 0.0401 / 4)^{4 n}$

Step 3 ： $A_{1} (10) = 20000 (1.0405)^{10} \approx 29714.47$ ; $A_{2} (10) = 20000 (1 + 0.0401 / 4)^{4 \times 10} \approx 29713.14$

Step 4 ：Option 1 will yield more money, the difference is approximately $29714.47 - 29713.14 \approx $ 1.33$