Let’s break down each option and see which is better **IF interest rates are expected to rise** in the year. ### The Options 1. **6% compounded annually for 4 years** 2. **5% compounded annually for 6 years** 3. **12% compounded annually for 2 years** ### Step 1: Calculate Future Value for Each Option **Formula:** \( FV = P(1 + r)^n \) where \( P = \$25,000 \), \( r \) = annual interest rate (as decimal), \( n \) = number of years. --- #### **Option 1: 6% for 4 years** \( FV = 25,000 \times (1 + 0.06)^4 \) \( FV = 25,000 \times (1.2625) \) \( FV = \$31,562.50 \) --- #### **Option 2: 5% for 6 years** \( FV = 25,000 \times (1 + 0.05)^6 \) \( FV = 25,000 \times (1.3401) \) \( FV = \$33,502.50 \) --- #### **Option 3: 12% for 2 years** \( FV = 25,000 \times (1 + 0.12)^2 \) \( FV = 25,000 \times (1.2544) \) \( FV = \$31,360 \) --- ### Step 2: Consider Rising Interest Rates If **interest rates are expected to rise**, you may want to **avoid locking your money for a long time at a lower rate**. This way, when rates do rise, you can reinvest at higher rates. - **Option 1 (4 years at 6%)**: You lock in for 4 years at 6%. If rates rise above 6%, you can't take advantage until after 4 years. - **Option 2 (6 years at 5%)**: You lock in for the longest period at the lowest rate. This is the *worst option* if rates rise. - **Option 3 (2 years at 12%)**: You lock in for only 2 years, and at the highest rate. After 2 years, when rates are expected to be even higher, you can reinvest at those higher rates. ### Step 3: Which is Better? - **In terms of future value over the stated term:** - Option 2 gives the most after its term (\$33,502.50), but locks you into the lowest rate for the longest time. - Option 3 gives you \$31,360 after 2 years, but then lets you reinvest at higher rates sooner. **If rates are expected to rise, the flexibility to reinvest at higher rates is valuable.** ### **Conclusion** **Option 3 (12% for 2 years)** is the best, **because:** - It gives you the highest short-term return. - You can reinvest after 2 years, potentially at even higher rates (taking advantage of the expected rise). - You avoid being locked into a lower rate for a longer period. **Option 2 is the worst choice if rates rise, as you are locked in for the longest time at the lowest rate.** --- **In summary:** > **Choose the 12% for 2 years.** > This gives you flexibility to reinvest at higher rates when they rise, maximizing your long-term returns.