a man earns ¡ê20000 per annum. he receives a 6% increase each day. how much does he earn after eight years? how many years does he take for jpgis salary to double?
I am sure you meant 6% each year, not each day
(at per day, the answer would be an absurdly large number)
after 1 year -- 20000(1.06)
after 2 years -- 20000(1.06)^2
..
after 8 years: amount = 20000(1.06)^8
= ....
To calculate the man's earnings after eight years, we can use the compound interest formula.
Let's break down the problem step by step:
1. Calculate the daily increase:
The man receives a 6% increase each day. To calculate the daily increase, we need to multiply his earnings by 6% (or 0.06). So, the daily increase is £20,000 x 0.06 = £1,200.
2. Calculate the annual increase:
Since there are 365 days in a year, the man's total annual increase can be calculated by multiplying the daily increase by 365. So, the annual increase is £1,200 x 365 = £438,000.
3. Calculate the total earnings after eight years:
To calculate the total earnings after eight years, we need to multiply the annual increase by the number of years. So, the total earnings after eight years are £438,000 x 8 = £3,504,000.
Now, let's calculate the number of years it takes for the man's salary to double.
1. Start with the initial salary: £20,000.
2. Calculate the new salary after one year using the formula:
New Salary = Initial Salary + (Initial Salary x 6%)
New Salary = £20,000 + (£20,000 x 0.06) = £21,200.
3. Repeat step 2 until the new salary is double the initial salary:
£21,200, £22,472, £23,811, £25,227, etc.
4. Continue calculating the new salary until it reaches or exceeds £40,000 (double the initial salary).
5. Count the number of years it took to reach or exceed £40,000 to find the answer.