Luna Chan
08/23/2024 · Primary School
What is Amir's savings on the 15 th day? 9. The salary of a professional footballer in the first year is RM2 000000 and the yearly increment is \( 4 \% \) of the previous year's salary. This means that in the second year. the athlete's salary is I. 04 times the previous year's salary. What is the athlete's salary in the 7th year? Give the answer to the nearest RM.
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Step-by-step Solution
To find Amir's savings on the 15th day, we need to know the initial amount he saved and the daily savings rate. However, the information provided does not include these details.
Next, let's calculate the athlete's salary in the 7th year based on the given information:
1. The salary of a professional footballer in the first year is RM2,000,000.
2. The yearly increment is 4% of the previous year's salary.
3. This means that in the second year, the athlete's salary is 1.04 times the previous year's salary.
To find the athlete's salary in the 7th year, we can calculate the salary increment for each year and then multiply the initial salary by the cumulative increment factor.
Let's calculate the athlete's salary in the 7th year step by step:
1. Calculate the salary increment for each year:
- Year 1: RM2,000,000
- Year 2: 1.04 * RM2,000,000
- Year 3: 1.04 * (1.04 * RM2,000,000)
- ...
- Year 7: 1.04^6 * RM2,000,000
2. Calculate the athlete's salary in the 7th year by multiplying the initial salary by the cumulative increment factor.
Let's calculate the athlete's salary in the 7th year.
Calculate the value by following steps:
- step0: Calculate:
\(1.04^{6}\times 2000000\)
- step1: Convert the expressions:
\(\left(\frac{26}{25}\right)^{6}\times 2000000\)
- step2: Multiply the terms:
\(2000000\left(\frac{26}{25}\right)^{6}\)
- step3: Simplify:
\(2000000\times \frac{26^{6}}{25^{6}}\)
- step4: Rewrite the expression:
\(15625\times 128\times \frac{26^{6}}{25^{6}}\)
- step5: Rewrite the expression:
\(25^{3}\times 128\times \frac{26^{6}}{25^{6}}\)
- step6: Reduce the numbers:
\(128\times \frac{26^{6}}{25^{3}}\)
- step7: Multiply:
\(\frac{128\times 26^{6}}{25^{3}}\)
- step8: Simplify:
\(\frac{128\times 26^{6}}{15625}\)
The athlete's salary in the 7th year is approximately RM2,530,638.04.
Therefore, the athlete's salary in the 7th year is RM2,530,638.04.
Quick Answer
The athlete's salary in the 7th year is approximately RM2,530,638.
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