Q: The income of a person is 3,00,000, in the first year and he receives an increase of 10,000 to his income per year for the next 19 years. Find the total mount, he received in 20 years. Currency = Dollars.
My solution:
According to the question , he receives an increment of 10,000 per year on his annual income = 3,00,000.
It’s like in 2nd year , income = $3,00,00$ + 10,000 = 3,10,000.
So , till 19 years. There is an increment in income. After that , amount is the same as the last one.
Payment at 19th year = 3,00,000 + 19*10,000 = 4,90,000.
I am guessing that even for 20th year , it is 4,90,000. No increment,
So , what we can do is find the sum for 20 years with 10,000 as increment & subtract 10,000 once we get the final sum since there is no increment for 20th year.
$S_{20}=\frac{20}{2}[600000+19 \times 10000]=10(790000)=79,00,000$
Answer is 78,90,000
But according to the solution of textbook. Answer is $79,00,000. They even counted another increment in 20th year.
I want to know where am I going wrong.
The part where you went wrong is stating: 'So , till 19 years. There is an increment in income. After that , amount is the same as the last one.' whereas in the question it is mentioned for the next 19 years which sums upto 20 years.