Sage decides to cash in all his savings to open a recording studio. He has three accounts to cash in. The first earned 9 percent for two years. The second earned 6 percent for three years. And the last earned 3 percent for six years. Supposing he started with $5,000 in each account, from which account will he get the most cash?

Question

a. The three-year account at 6 percent
b. The accounts are all worth the same.
c. The six-year account at 3 percent
d. The two-year account at 9 percent

Answer 1

To determine which account Sage will get the most cash from, we need to calculate the future value of each account using the formula for compound interest:

\[ A = P(1 + r)^n \] where:

• \( A \) is the amount of money accumulated after n years, including interest.
• \( P \) is the principal amount (the initial amount of money),
• \( r \) is the annual interest rate (decimal),
• \( n \) is the number of years the money is invested or borrowed for.

Let's calculate the future value for each account:

1. First account (9% for 2 years): \[ P = 5000, \quad r = 0.09, \quad n = 2 \] \[ A = 5000(1 + 0.09)^2 = 5000(1.09)^2 = 5000 \times 1.1881 \approx 5940.50 \]

2. Second account (6% for 3 years): \[ P = 5000, \quad r = 0.06, \quad n = 3 \] \[ A = 5000(1 + 0.06)^3 = 5000(1.06)^3 = 5000 \times 1.191016 \approx 5955.08 \]

3. Third account (3% for 6 years): \[ P = 5000, \quad r = 0.03, \quad n = 6 \] \[ A = 5000(1 + 0.03)^6 = 5000(1.03)^6 = 5000 \times 1.194052 \approx 5970.26 \]

Now we compare the amounts:

• First account (9% for 2 years): $5940.50
• Second account (6% for 3 years): $5955.08
• Third account (3% for 6 years): $5970.26

Based on these calculations, the third account at 3% for 6 years will yield the most cash.

Therefore, the correct answer is: c. The six-year account at 3 percent