Question

Charlie has $14,000 to invest for a period of 5 years. The following three alternatives are available to him:

• Account 1 pays 5.00% for year 1, 7.00% for year 2, 8.00% for year 3. 11.00% for year 4, and 12.00% for year 5, all with annual
compounding. • Account 2 pays 12.00% for year 1. 11.00% for year 2, 8.00% for year 3, 7.00% for year 4, and 5.00% for year 5, all with annual compounding.
• Account 3 pays interest at the rate of 8.56944% per year for all 5 years.
Based on the available balance at the end of year 5, which alternative is Charlie's best choice?
Year 5 Balance, Alternative 1: $
Year 5 Balance, Alternative 2: $
Year 5 Balance, Alternative 3: $
Carry all interim calculations to 5 decimal places and then round your final answer to the nearest dollar. The tolerance is ±5

Answer 1

At the end of year 5, Charlie's best choice among the given alternatives is Account 1 with a balance of $22,316.

Step-by-step explanation:

To determine the best investment choice, we'll calculate the year 5 balances for each alternative and compare them.

For Account 1:

Using the formula for compound interest, A = P(1 + r/n)^(nt), where A is the amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

For Account 1:

Year 5 Balance = $14,000 * (1 + 0.12)^5 = $22,316.16 (rounded to the nearest dollar).

For Account 2:

Calculating the year 5 balance for Account 2 using the same formula:

Year 5 Balance = $14,000 * (1 + 0.05) * (1 + 0.11) * (1 + 0.08) * (1 + 0.07) * (1 + 0.12) = $22,258.56.

For Account 3:

Account 3 offers a consistent interest rate of 8.56944% per year for all 5 years. Using the formula:

Year 5 Balance = $14,000 * (1 + 0.0856944)^5 = $22,053.76.

Comparing the Year 5 Balances:

Account 1 yields the highest balance at the end of 5 years, amounting to $22,316. This exceeds the balances of Account 2 ($22,258) and Account 3 ($22,053). Therefore, the most lucrative option for Charlie among the given alternatives is Account 1.