Lilah has $7,000 to invest for 5 years. Investment Option C offers a 3.2% annual interest rate compounded quarterly, while Option D offers the same rate but compounded continuously. What is the exact total amount Lilah will have in each investment option after 5 years? Compound Interest Formula: A=P(1+(r)/(n))^nt Continuously Compounded Interest Formula: A=Pe^rt The value of e , also known as Euler's number, is approximately 2.71828
Answer
A
Option C: 8 dollars comma 209 point 3 5, Option D: 8 dollars comma 214 point 5 8
B
Option C: 8 dollars comma 214 point 5 8, Option D: 8 dollars comma 209 point 3 5
C
Option C: 8 dollars comma 200 point 0 0, Option D: 8 dollars comma 210 point 0 0
D
Option C: 8 dollars comma 210 point 0 0, Option D: 8 dollars comma 220 point 0 0
Explanation
For Option C, use quarterly compounding: A = 7000(1 + 0.032/4)^(4 × 5) = 7000(1.008)^20 ≈ $8,209.35. For Option D, use continuous compounding: A = 7000e^(0.032 × 5) = 7000e^0.16 ≈ $8,214.58. These amounts match the choice stating Option C is $8,209.35 and Option D is $8,214.58.
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