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You saved R4 750 during the last year. You decide that it will be the best to invest the money. At your local bank they have two investment options: Option 1: A 5 Year foxed deposit with \( 3.25 \% \) simple interest per year. Option 2: A 5 Year foxed deposit with \( 3.10 \% \) compound interest per year. Which 5 year investment will be the best?

Ask by Nguyen King. in South Africa
Feb 03,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

Option 2, the 5-year fixed deposit with 3.10% compound interest, is the better investment choice as it yields approximately R11.40 more than Option 1 after 5 years.

Solution

To determine which investment option is better after 5 years, let's calculate the future value for both options using the provided interest rates. ### **Option 1: Simple Interest** - **Principal (P)**: R4,750 - **Interest Rate (r)**: 3.25% per year (0.0325 in decimal) - **Time (t)**: 5 years **Formula for Simple Interest:** \[ A = P \times (1 + r \times t) \] **Calculation:** \[ A_1 = 4,750 \times (1 + 0.0325 \times 5) = 4,750 \times 1.1625 = R5,521.88 \] ### **Option 2: Compound Interest** - **Principal (P)**: R4,750 - **Interest Rate (r)**: 3.10% per year (0.031 in decimal) - **Time (t)**: 5 years **Formula for Compound Interest:** \[ A = P \times (1 + r)^t \] **Calculation:** \[ A_2 = 4,750 \times (1 + 0.031)^5 \] First, calculate \((1 + 0.031)^5\): \[ (1.031)^5 \approx 1.1649 \] Now, multiply by the principal: \[ A_2 = 4,750 \times 1.1649 \approx R5,533.28 \] ### **Comparison:** - **Option 1 (Simple Interest)**: R5,521.88 - **Option 2 (Compound Interest)**: R5,533.28 **Difference:** R5,533.28 (Option 2) - R5,521.88 (Option 1) ≈ R11.40 ### **Conclusion:** **Option 2**, the **5-year fixed deposit with 3.10% compound interest**, yields approximately R11.40 more than Option 1 after 5 years. Although the difference is relatively small, Compound Interest provides a slightly better return in this scenario. **Recommendation:** Choose **Option 2** for a better return on your investment.

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The Deep Dive

Let's break it down! For Option 1, with simple interest, you can calculate your earnings with the formula: \( A = P(1 + rt) \). Here, \( P \) is R4,750, \( r \) is 0.0325, and \( t \) is 5 years. This means you'll end up with about R5,762.50 after the 5 years. Now for Option 2, the compound interest formula is: \( A = P(1 + r)^t \). So for this investment, once you plug in your numbers: \( A = 4750(1 + 0.031)^5 \), you'll end up with roughly R5,623.65. Thus, Option 1 with simple interest gives you better returns after 5 years! Make sure to review your calculations and consider any potential fees from the bank, as they can influence your final amount. Always double-check the fine print before making a decision!

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