Ramesh purchased a home with the
help of a bank loan. He plans to pay
back the entire debt of Rs. 3,30,600
in monthly instalments, beginning
with the first instalment of Rs. 5,000.
He then decided to increase the
instalment amount every month by
200 which forms an AP. It will take
him 38 months to repay the loan in
this manner.
Based on the above
information, answer the following
questions
(i) How much money will he pay in her 25 instalment?
(ii) In which month he will pay rs. 8000 to
the bank as an instalment?
(iii) How much money would be paid till the 30th instalment to the bank?
(iv)In how many months he will pay rs. 1,38,000 to the bank?
To find the answers to the questions, we need to analyze the given information and calculate the values based on the given series.
The given information states that Ramesh will repay the entire debt of Rs. 3,30,600 in monthly installments. The first installment is Rs. 5,000, and each subsequent installment is increased by Rs. 200, forming an arithmetic progression (AP). It will take him 38 months to repay the loan in this manner.
Let's break down the given information to solve the questions one by one:
(i) To find how much money Ramesh will pay in her 25th installment, we need to calculate the value of the 25th term of the arithmetic progression.
The formula to find the nth term of an arithmetic progression is:
nth term = a + (n - 1)d
where,
a = First term of the AP
n = Number of terms
d = Common difference between consecutive terms
In this case:
a = 5000 (first installment)
n = 25 (25th installment)
d = 200 (common difference)
Using the formula, we can calculate the 25th term:
25th term = 5000 + (25 - 1) * 200
= 5000 + 24 * 200
= 5000 + 4800
= 9800
Therefore, Ramesh will pay Rs. 9,800 in his 25th installment.
(ii) To find in which month he will pay Rs. 8,000 to the bank as an installment, we need to determine the term of the AP that corresponds to Rs. 8,000.
Using the formula mentioned above, we can calculate the term as follows:
8000 = 5000 + (n - 1) * 200
3000 = (n - 1) * 200
Divide both sides by 200:
15 = n - 1
n = 15 + 1
n = 16
Therefore, Ramesh will pay Rs. 8,000 to the bank in the 16th month as an installment.
(iii) To find how much money would be paid till the 30th installment to the bank, we need to calculate the sum of the first 30 terms of the AP.
The formula to calculate the sum of the first n terms of an arithmetic progression is:
Sum of n terms = (n/2) * [2a + (n - 1)d]
In this case:
a = 5000 (first installment)
n = 30 (30 installments)
d = 200 (common difference)
Using the formula, we can calculate the sum of the first 30 terms:
Sum of 30 terms = (30 / 2) * [2 * 5000 + (30 - 1) * 200]
= 15 * [10000 + 29 * 200]
= 15 * [10000 + 5800]
= 15 * 15800
= 237000
Therefore, Ramesh would have paid Rs. 2,37,000 to the bank until the 30th installment.
(iv) To find in how many months he will pay Rs. 1,38,000 to the bank, we need to calculate the term number for this payment amount.
Using the formula mentioned earlier, we can calculate the term as follows:
138000 = 5000 + (n - 1) * 200
138000 - 5000 = (n - 1) * 200
133000 = 200(n - 1)
Divide both sides by 200:
665 = n - 1
n = 665 + 1
n = 666
Therefore, Ramesh will pay Rs. 1,38,000 to the bank in the 666th month.
I hope this explanation helps you understand how to solve the given questions based on the given information.