NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 1(iv)
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 1 (iv)
Question:
In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? The amount of money in the account every year, when Rs 10000 is deposited at compound interest at 8 % per annum.
Given:
Rs 10000 is deposited at compound interest at 8% per annum.
To Find:
Whether the amount of money in the account each year forms an arithmetic progression.
Formula:
Compound Interest Formula: A = P (1 + r/n)nt
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
Solution:
Let's calculate the amount for the first few years:
Year 1: A = 10000 (1 + 0.08)1 = 10800
Year 2: A = 10000 (1 + 0.08)2 = 11664
Year 3: A = 10000 (1 + 0.08)3 = 12597.12
The differences between consecutive years are:
Year 2 - Year 1 = 11664 - 10800 = 864
Year 3 - Year 2 = 12597.12 - 11664 = 933.12
Since the differences are not constant, the amounts do not form an arithmetic progression.
Result:
No, the amounts do not form an arithmetic progression. Compound interest grows exponentially, not linearly.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 2 (i).
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