Question

Consider the pair of savings plans below. Compare the balances in each plan after 14 years. Which person deposited more money in the​ plan? Which of the two investment strategies is​ better? Assume that the compounding and payment periods are the same for each pair. Kerry deposits ​$ 30 per month in an account with an APR of 4 ​%, while Sage deposits ​$100 per quarter in an account with an APR of ​4.5%.

Answer 1

Kerry deposited $5,040 in 14 years, while Sage deposited $5,600. Sage's investment strategy is better because their balance after 14 years is $8,006.15 compared to Kerry's $7,902.53.

Step-by-step explanation:

To compare the balances in each plan after 14 years, we first need to understand how much money Kerry and Sage have deposited. Kerry deposited $30 per month for 14 years, which is equal to a total deposit of $30 * 12 months * 14 years = $5,040. Sage deposited $100 per quarter for 14 years, which is equal to a total deposit of $100 * 4 quarters * 14 years = $5,600.

Now, let's calculate the balances in each plan. Kerry's account has an APR of 4%, so we can use the compound interest formula to find the balance after 14 years: $5,040 * (1 + 0.04/12)^(12*14) = $7,902.53. Sage's account has an APR of 4.5%, so we can use the same formula to find the balance after 14 years: $5,600 * (1 + 0.045/4)^(4*14) = $8,006.15.

Based on these calculations, Sage deposited more money in the plan ($5,600 compared to Kerry's $5,040), and Sage's investment strategy is better because their balance after 14 years is also higher ($8,006.15 compared to Kerry's $7,902.53).