ICSE Solutions for Selina Concise Chapter 2 Banking (Recurring Deposit Accounts) Class 10 Maths
Exercise 2(A)
1. Manish opens a Recurring Deposit Account with the Bank of Rajasthan and deposits Rs. 600 per month for 20 months. Calculate the maturity value of this account, if the bank pays interest at the rate of 10% per annum.
Solution
From the question, we have
Installment per month (P) = Rs 600
Number of months (n) = 20
Rate of interest(r) = 10% p.a.
So,
S.I = Rs 1,050
∴ The amount that Manish will be getting at the time of maturity is
= Rs (600 × 20) + 1,050
= Rs 12,000 + 1,050
= Rs 13,050
2. Mrs. Mathew opened a Recurring Deposit Account in a certain bank and deposited Rs. 640 per month for 41/2 years. Find the maturity value of this account, if the bank pays interest at the rate of 12% per year.
Solution
Installment per month (P) = Rs 640
Number of months (n) = 54
Rate of interest (r) = 12% p.a.
So,
S.I. = Rs 9,504
∴ The amount that Mrs. Mathew will be getting at the time of maturity is
= Rs (640 × 54)+ Rs 9,504
= Rs 34,560 + Rs 9,504
= Rs 44,064
3. Each of A and B both opened recurring deposit accounts in a bank. If A deposited Rs 1,200 per month for 3 years and B deposited Rs 1,500 per month for 2½ years; find, on maturity, who will get more amount and by how much? The rate of interest paid by the bank is 10% per annum.
Solution
Calculating for A:
Installment per month (P) = Rs 1,200
Number of months (n) = 36
Rate of interest (r) = 10% p.a.
So,
S.I = Rs 6,660
Hence,
The amount that A will be getting at the time of maturity is
= Rs (1,200×36) + Rs 6,660
= Rs 43,200 + Rs 6,660
= Rs 49,860
Calculating for B:
Installment per month (P) = Rs1,500
Number of months (n) = 30
Rate of interest(r) = 10% p.a.
So,
S.I = Rs 5,812.50
Hence,
The amount that B will be getting at the time of maturity is
= Rs (1,500 × 30) + Rs 5,812.50
= Rs 45,000 + Rs 5,812.50
= Rs 50,812.50
Now,
Difference between both the amounts is = Rs 50,812.50 – Rs 49,860
= Rs 952.50
∴ B will get more amount than A by Rs 952.50
4. Ashish deposits a certain sum of money every month is a Recurring Deposit Account for a period of 12 months. If the bank pays interest at the rate of 11% p.a. and Ashish gets Rs 12,715 as the maturity value of this account, what sum of money did he pay every month?
Solution
Let us assume the installment per month (P) as Rs y
Number of months (n) = 12
Rate of interest (r) = 11%p.a.
So,
S.I = Rs 0.715y
Hence,
The amount at maturity will be = Rs (y × 12) + Rs 0.715y = Rs 12.715y
Given that the maturity value = Rs 12,715
So, on equating we have
Rs 12.715y = Rs 12,715
y = 12,715/ 12.715 = Rs 1,000
∴ the sum of money paid by Ashish every month is Rs 1,000
5. A man has a Recurring Deposit Account in a bank for 3½ years. If the rate of interest is 12% per annum and the man gets Rs 10,206 on maturity, find the value of monthly installments.
Solution
Let’s assume that the installment per month (P) = Rs y
Number of months (n) = 42
Rate of interest (r) = 12% p.a.
So,
S.I = Rs 9.03y
Hence,
The amount at maturity will be = Rs (y × 42) + Rs 9.03y = Rs 51.03y
But given maturity value = Rs10,206
So, on equating we have
Rs 51.03y = Rs 10206
y = 10206/ 51.03 = Rs 200
∴ the value of monthly installment is Rs 200
Exercise 2(B)
1. Pramod deposits Rs 600 per month in a Recurring Deposit Account for 4 years. If the rate of interest is 8% per year; calculate the maturity value of his account.
Solution
Given,
Installment per month (P) = Rs 600
Number of months (n) = 48
Rate of interest (r) = 8% p.a.
So,
S.I = Rs 4,704
Hence,
The amount that Pramod will be getting at the time of maturity is
= Rs (600 × 48) + Rs 4,704
= Rs 28,800 + Rs 4,704
= Rs 33,504
2. Ritu has a Recurring Deposit Account in a bank and deposits Rs 80 per month for 18 months. Find the rate of interest paid by the bank if the maturity value of account is Rs 1,554.
Solution
Given,
Installment per month (P) = Rs 80
Number of months (n) = 18
Let rate of interest (r) = r % p.a.
S.I = 11.4r
Hence, the amount at the time of maturity will be = Rs (80 × 18) + Rs (11.4r)
And given maturity value = Rs 1,554
So, on equating
Rs (80 × 18) + Rs (11.4r) = Rs 1,554
11.4r = Rs 1,554 – Rs 1,440
r = 114/ 11.4 = 10 %
∴ the rate of interest paid by the bank is 10 %
3. The maturity value of a R.D. Account is Rs 16,176. If the monthly installment is Rs 400 and the rate of interest is 8%; find the time (period) of this R.D Account.
Solution
Given,
Installment per month (P) = Rs 400
Let the time, number of months (n) = n
Rate of interest (r) = 8 % p.a.
So, at the time of maturity the value will be = Rs (400 × n)+ Rs 4n(n + 1)/3
And, given maturity value = Rs 16,176
So, on equating
Rs (400× n) + 4n(n + 1)/3 = Rs 16,176
1200n +4n2 + 4n = Rs 48,528
4n2 + 1204n = Rs 48,528
n2 + 301n – 12132 = 0
(n + 337)(n – 36) = 0
n = -337 (not considered as time cannot be negative) or n = 36
∴ the number of months (time) = 36 months = 3years
4. Mr. Bajaj needs Rs 30,000 after 2 years. What least money (in multiple of Rs 5) must he deposit every month in a recurring deposit account to get required money after 2 years, the rate of interest being 8% p.a.?
Solution
Let’s assume the installment per month to be Rs P
Number of months (n) = 24
Rate of interest = 8% p.a.
So,
S.I = Rs 2P
Thus,
The amount at maturity will be = Rs (P × 24) + Rs 2P = Rs 26P
And, given maturity value = Rs30,000
So, on equating
Rs 26P = Rs 30,000
P = 30,000/ 26
P = Rs 1,153.84 = Rs 1,155(multiple of 5)
5. Mr. Richard has a recurring deposit account in a post office for 3 years at 7.5 % p.a. simple interest. If he gets Rs. 8,325 as interest at the time of maturity, find:
(i) the monthly instalment
(ii) the amount of maturity
Solution
Let’s assume the monthly installment be Rs P
Interest over the period = Rs. 8,325
Rate of interest = 7.5%
Time = 3 years = 36 months
(i)
∴ the monthly installment is Rs 2,000
(ii) Maturity value = total sum deposited + interest
= 2000 × 36 + 8325
= 72000+ 8325
= Rs 80,325
∴ the amount of maturity is Rs 80,325