## Selina Concise Mathematics Class 10 ICSE Solutions Banking (Recurring Deposit Accounts)

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**Selina ICSE Solutions for Class 10 Maths Chapter 2 Banking (Recurring Deposit Accounts)**

**Exercise 2(A)**

**Question 1.**

Manish opens a Recurring Deposit Account with the Bank of Rajasthan and deposits ₹ 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:**

Installment per month(P) = ₹ 600

Number of months(n) = 20

Rate of interest(r) = 10% p.a.

The amount that Manish will get at the time of maturity

= ₹ (600×20) + ₹ 1,050

= ₹ 12,000 + ₹ 1,050

= ₹ 13,050

**Question 2.**

Mrs. Mathew opened a Recurring Deposit Account in a certain bank and deposited ₹ 640 per month for 4 ½ 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) = ₹ 640

Number of months(n) = 54

Rate of interest(r)= 12% p.a.

The amount that Manish will get at the time of maturity

= ₹ (640×54)+ ₹ 9,504

= ₹ 34,560 + ₹ 9,504

= ₹ 44,064

**Question 3.**

Each of A and B both opened recurring deposit accounts in a bank. If A deposited ₹ 1,200 per month for 3 years and B deposited ₹ 1,500 per month for 2 ½ 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:**

For A

Installment per month(P) = ₹ 1,200

Number of months(n) = 36

Rate of interest(r) = 10% p.a.

The amount that A will get at the time of maturity

= ₹ (1,200×36) + ₹ 6,660

= ₹ 43,200 + ₹ 6,660

= ₹ 49,860

For B

Instalment per month(P) = ₹ 1,500

Number of months(n) = 30

Rate of interest(r) = 10% p.a.

The amount that B will get at the time of maturity

= ₹ (1,500×30) + ₹ 5,812.50

= ₹ 45,000 + ₹ 5,812.50

= ₹ 50,812.50

Difference between both amounts = ₹ 50,812.50 – ₹ 49,860

= ₹ 952.50

Then B will get more money than A by ₹ 952.50.

**Question 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 ₹ 12,715 as the maturity value of this account, what sum of money did money did he pay every month?

**Solution:**

Let Installment per month(P) = ₹ y

Number of months(n) = 12

Rate of interest(r) = 11% p.a.

Maturity value = ₹ (y × 12) + ₹ 0.715y = ₹ 12.715y

Given maturity value = ₹ 12,715

Then ₹ 12.715y = ₹ 12,715

**Question 5.**

A man has a Recurring Deposit Account in a bank for 3 ½ years. If the rate of interest is 12% per annum and the man gets ₹ 10,206 on maturity, find the value of monthly instalments.

**Solution:**

Let Installment per month(P) = ₹ y

Number of months(n) = 42

Rate of interest(r) = 12% p.a.

Maturity value= ₹ (y × 42) + ₹ 9.03y= ₹ 51.03y

Given maturity value = ₹ 10,206

Then ₹ 51.03y = ₹ 10206

**Question 6.**

(i) Puneet has a Recurring Deposit Account in the Bank of Baroda and deposits ₹ 140 per month for 4 years. If he gets ₹ 8,092 on maturity, find the rate of interest given by the bank.

(ii) David opened a Recurring Deposit Account in a bank and deposited ₹ 300 per month for two years. If he received ₹ 7,725 at the time of maturity, find the rate of interest per annum.

**Solution:**

(a)

Installment per month(P) = ₹ 140

Number of months(n) = 48

Let rate of interest(r) = r% p.a.

Maturity value= ₹ (140 × 48) + ₹ (137.20)r

Given maturity value = ₹ 8,092

Then ₹ (140 × 48) + ₹ (137.20)r = ₹ 8,092

⇒ 137.20r = ₹ 8,092 – ₹ 6,720

(b)

Instalment per month(P) = ₹ 300

Number of months(n) = 24

Let rate of interest(r)= r% p.a.

Maturity value = ₹ (300 × 24) + ₹ (75)r

Given maturity value = ₹ 7,725

Then ₹ (300 × 24) + ₹ (75)r = ₹ 7,725

⇒ 75 r = ₹ 7,725 – ₹ 7,200

**Question 7.**

Amit deposited ₹ 150 per month in a bank for 8 months under the Recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month?

**Solution:**

Installment per month(P) = ₹ 150

Number of months(n) = 8

Rate of interest(r) = 8% p.a.

The amount that Manish will get at the time of maturity

= ₹ (150 × 8) + ₹ 36

= ₹ 1,200 + ₹ 36

= ₹ 1,236

**Question 8.**

Mrs. Geeta deposited ₹ 350 per month in a bank for 1 year and 3 months under the Recurring Deposit Scheme. If the maturity value of her deposits is ₹ 5,565; find the rate of interest per annum.

**Solution:**

Installment per month(P) = ₹ 350

Number of months(n) = 15

Let rate of interest(r)= r% p.a.

Maturity value= ₹ (350 × 15) + ₹ (35)r

Given maturity value = ₹ 5,565

Then ₹ (350 × 15) + ₹ (35)r = ₹ 5,565

⇒ 35r = ₹ 5,565 – ₹ 5,250

**Question 9.**

A recurring deposit account of ₹ 1,200 per month has a maturity value of ₹ 12,440. If the rate of interest is 8% and the interest is calculated at the end of every month; find the time (in months) of this Recurring Deposit Account.

**Solution:**

Installment per month(P) = ₹ 1,200

Number of months(n) = n

Let rate of interest(r) = 8% p.a.

Maturity value = ₹ (1,200 × n) + ₹ 4n(n+1) = ₹ (1200n+4n^{2}+4n)

Given maturity value= ₹ 12,440

Then 1200n+4n^{2}+4n = 12,440

Then number of months = 10

**Question 10.**

Mr. Gulati has a Recurring Deposit Account of ₹ 300 per month. If the rate of interest is 12% and the maturity value of this account is ₹ 8,100; find the time (in years) of this Recurring Deposit Account.

**Solution:**

Installment per month(P) = ₹ 300

Number of months(n) = n

Let rate of interest(r)= 12% p.a.

Maturity value= ₹ (300 × n)+ ₹ 1.5n(n+1)

= ₹ (300n+1.5n^{2}+1.5n)

Given maturity value= ₹ 8,100

Then 300n+1.5n^{2}+1.5n = 8,100

Then time = 2 years.

**Question 11.**

Mr. Gupta opened a recurring deposit account in a bank. He deposited ₹ 2,500 per month for two years. At the time of maturity he got ₹ 67,500. Find:

(i) the total interest earned by Mr. Gupta

(ii) the rate of interest per annum.

**Solution:**

(i)

Maturity value = ₹ 67,500

Money deposited = ₹ 2,500 × 24= ₹ 60,000

Then total interest earned = ₹ 67,500 – ₹ 60,000 = ₹ 7,500 Ans.

(ii)

Installment per month(P) = ₹ 2,500

Number of months(n) = 24

Let rate of interest(r)= r% p.a.

**Exercise 2(B)**

**Question 1.**

Pramod deposits ₹ 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:**

Installment per month(P) = ₹ 600

Number of months(n) = 48

Rate of interest(r)= 8% p.a.

The amount that Manish will get at the time of maturity

= ₹ (600 × 48) + ₹ 4,704

= ₹ 28,800 + ₹ 4,704

= ₹ 33,504

**Question 2.**

Ritu has a Recurring Deposit Account in a bank and deposits ₹ 80 per month for 18 months. Find the rate of interest paid by the bank if the maturity value of account is ₹ 1,554.

**Solution:**

Installment per month(P) = ₹ 80

Number of months(n) = 18

Let rate of interest(r) = r% p.a.

Maturity value = ₹ (80 × 18) + ₹ (11.4r)

Given maturity value = ₹ 1,554

Then ₹ (80 × 18 ) + ₹ (11.4r) = ₹ 1,554

⇒ 11.4r = ₹ 1,554 – ₹ 1,440

**Question 3.**

The maturity value of a R.D. Account is ₹ 16,176. If the monthly installment is ₹ 400 and the rate of interest is 8%; find the time (period) of this R.D Account.

**Solution:**

Installment per month(P) = ₹ 400

Number of months(n) = n

Let rate of interest(r)= 8% p.a.

⇒ 1200n +4n^{2}+4n= ₹ 48,528

⇒ 4n^{2}+1204n = ₹ 48,528

⇒ n^{2}+301n – 12132= 0

⇒ (n+337)(n-36)=0

⇒ n = -337 or n=36

Then number of months = 36 months = 3 years

**Question 4.**

Mr. Bajaj needs ₹ 30,000 after 2 years. What least money (in multiple of 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 installment per month = ₹ P

Number of months(n) = 24

Rate of interest = 8% p.a.

Maturity value = ₹ (P × 24)+ ₹ 2P = ₹ 26P

Given maturity value = ₹ 30,000

**Question 5.**

Rishabh has recurring deposit account in a post office for 3 years at 8% p.a. simple interest. If he gets ₹ 9,990 as interest at the time of maturity, find:

(i) The monthly installment.

(ii) The amount of maturity.

**Solution:**

Let Installment per month = ₹ P

Number of months(n) = 36

Rate of interest(r)= 8% p.a.

Given interest = ₹ 9,990

(ii) Maturity value = ₹ (2,250 × 36) + ₹ 9,990 = ₹ 90,990

**Question 6.**

Gopal has a cumulative deposit account and deposits ₹ 900 per month for a period of 4 years he gets ₹ 52,020 at the time of maturity, find the rate of interest.

**Solution:**

Installment per month(P) = ₹ 900

Number of months(n) = 48

Let rate of interest(r)= r% p.a.

Maturity value= ₹ (900 × 48) + ₹ (882)r

Given maturity value = ₹ 52,020

Then ₹ (900 × 48) + ₹ (882)r = ₹ 52,020

⇒ 882r = ₹ 52,020 – ₹ 43,200

**Question 7.**

Deepa has a 4-year recurring deposit account in a bank and deposits ₹ 1,800 per month. If she gets ₹ 1,08,450 at the time of maturity, find the rate of interest.

**Solution:**

Installment per month(P) = ₹ 1,800

Number of months(n) = 48

Let rate of interest(r)= r% p.a.

Maturity value = ₹ (1,800 x 48) + ₹ (1,764)r

Given maturity value = ₹ 1,08,450

Then ₹ (1,800 x 48) + ₹ (1764)r = ₹ 1,08,450

⇒ 1764r = ₹ 1,08,450 – ₹ 86,400

**Question 8.**

Mr. Britto deposits a certain sum of money each month in a Recurring Deposit Account of a bank. If the rate of interest is of 8% per annum and Mr. Britto gets Rs. 8,088 from the bank after 3 years, find the value of his monthly instalment.

**Solution:**

**Question 9.**

**Solution:**

**Question 10.**

Peter has a recurring deposit account in Punjab National Bank at Sadar Bazar, Delhi for 4 years at 10% p.a. He will get ₹ 6,370 as interest on maturity. Find :

(i) monthlyinstallment,

(ii) the maturity value of the account.

**Solution:**

**Question 11.**

Katrina opened a recurring deposit account with a Nationalised Bank for a period of 2 years. If the bank pays interest at the rate of 6% per annum and the monthly installment is ₹ 1,000, find the :

(i) interest earned in 2 years

(ii) maturity value

**Solution:**

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