To determine which type of automatic inflation protection will provide the greatest benefit increases, let's analyze each option carefully:
1. 5% Simple Interest:
- Simple interest means that the interest is calculated only on the principal amount. For an initial amount of 100, a 5% simple interest over one year would be:
[tex]\[
\text{Simple Interest} = 100 \times (1 + 0.05) = 100 \times 1.05 = 105
\][/tex]
- Therefore, the amount after one year would be 105.
2. 5% Compound Interest:
- Compound interest means that the interest is calculated on the principal amount as well as the accumulated interest over previous periods. For an initial amount of 100, a 5% compound interest over one year with annual compounding would be:
[tex]\[
\text{Compound Interest Annual} = 100 \times (1 + 0.05)^1 = 100 \times 1.05 = 105
\][/tex]
- Therefore, the amount after one year would still be 105, the same as the simple interest in this particular case. However, compounding interest more frequently could yield higher returns.
3. Monthly Compounding:
- If we compound the interest monthly, the interest rate is divided by 12 (months) and applied each month. For an initial amount of 100, with a 5% annual interest rate compounded monthly, the formula is:
[tex]\[
\text{Monthly Compounding} = 100 \times \left(1 + \frac{0.05}{12}\right)^{12}
\][/tex]
- Let's calculate this:
[tex]\[
\text{Monthly Compounding} = 100 \times \left(1 + \frac{0.05}{12}\right)^{12} \approx 100 \times 1.05116 \approx 105.12
\][/tex]
- Therefore, the amount after one year would be approximately 105.12, slightly higher than 105.
4. Annual Compounding:
- Annual compounding means the interest is calculated once a year, which we've already calculated under 5% compound interest. For an initial amount of 100 with a 5% annual interest rate compounded annually, it would be the same as 5% compound interest:
[tex]\[
\text{Annual Compounding} = 100 \times (1 + 0.05)^1 = 100 \times 1.05 = 105
\][/tex]
- Therefore, the amount after one year would be 105.
Comparing all options:
- Simple interest (105)
- Compound interest annually (105)
- Monthly compounding (105.12)
- Annual compounding (105)
The best option, which provides the greatest benefit increases over time, is the one with monthly compounding.
Therefore, the answer is:
C. Monthly
