Question

write each as an expression and simplify.

1. an investment of $500 doubles monthly for 2 years.
2. an investment of $1,000 tripled quarterly for 2 years.
3. an investment of $5,000 triples every 6 months for 2 years.
4. which is the best investment? circle the correct choice.

1 2 3

Explanation:

Step1: Calculate the number of periods for each investment

• For investment 1: 2 years = 24 months. Since it doubles monthly, the number of periods \(n_1=24\).
• For investment 2: 2 years = 8 quarters. Since it triples quarterly, the number of periods \(n_2 = 8\).
• For investment 3: 2 years = 4 half - years. Since it triples every 6 months, the number of periods \(n_3=4\).

Step2: Use the compound - growth formula \(A = P\times r^n\) (where \(P\) is the principal, \(r\) is the growth factor per period, and \(n\) is the number of periods)

• Investment 1: \(P_1=\$500\), \(r_1 = 2\) (doubles), \(n_1=24\)

\(A_1=500\times2^{24}\)
\(A_1=500\times16777216=\$8388608000\)

• Investment 2: \(P_2 = \$1000\), \(r_2=3\) (triples), \(n_2 = 8\)

\(A_2=1000\times3^{8}\)
\(A_2=1000\times6561=\$6561000\)

• Investment 3: \(P_3=\$5000\), \(r_3 = 3\) (triples), \(n_3=4\)

\(A_3=5000\times3^{4}\)
\(A_3=5000\times81=\$405000\)

Answer:

The best investment is 1.