A person deposit Rs 1000 in the first month the overy month he increase the monthly deposited by Rs 60 calculate his total investment at the end of 2 years
To calculate the total investment at the end of 2 years, we need to find the sum of a series. The series represents the monthly deposits made over the course of 2 years.
The formula to find the sum of a series is:
S = (n/2) * (a + l)
where:
S = sum of the series
n = number of terms in the series
a = first term of the series
l = last term of the series
In this case, the first term (a) is Rs 1000, and the monthly increase is Rs 60. Therefore, the last term (l) can be calculated as:
l = a + (n-1) * d
where:
d = common difference between consecutive terms
In this case, the common difference (d) is Rs 60, and the number of terms (n) is 24 (as there are 12 months in a year and we are calculating for 2 years).
Let's calculate the last term:
l = 1000 + (24-1) * 60
l = 1000 + 1380
l = 2380
Now, we can calculate the sum of the series using the formula:
S = (n/2) * (a + l)
S = (24/2) * (1000 + 2380)
S = 12 * 3380
S = 40,560
Therefore, the total investment at the end of 2 years is Rs 40,560.
To calculate the total investment at the end of 2 years, we need to calculate the sum of the monthly deposits over the 24 months and add the initial deposit of Rs 1000.
Here's how you can calculate it step-by-step:
1. Calculate the total number of months in 2 years: 2 years = 24 months.
2. Calculate the sum of an arithmetic series for the monthly deposits:
The first term (a) is Rs 1000, and the common difference (d) is Rs 60.
The formula to calculate the sum of an arithmetic series is: Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the series and n is the number of terms.
Plugging in the values, we get:
Sn = (24/2)(2 * 1000 + (24-1) * 60)
= (12)(2000 + 1380)
= 12 * 3380
= 40560
3. Add the initial deposit of Rs 1000 to the sum of the monthly deposits:
Total investment = 40560 + 1000
= 41560
Therefore, the person's total investment at the end of 2 years would be Rs 41,560.
Are you using this in India
You have an AP with
a = 1000
d = 60
You want the sum after 24 months, which is, using the usual formula:
S24 = 24/2 (2a+23d)
Now just crank it out