**Question 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 :**It is given that,

Deposit per month (P) = Rs. 600

Number of months (n) = 20

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

**Calculation of Simple Interest on Recurring Deposit:-**

**Calculation of maturity value:-**Amount of maturity value = Principle Amount + Interest

Amount of maturity value = Rs. (600 × 20) + Rs. 1050

Amount of maturity value = Rs. 12,000 + Rs. 1050

Amount of maturity value = Rs. 13,050

**Question 2. Mrs. Mathew opened a Recurring Deposit Account in a certain bank and deposited Rs. 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 :**It is given that,

Deposit per month (P) = Rs. 640

Number of months (n) = 54

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

**Calculation of Simple Interest on Recurring Deposit:-**

**Calculation of maturity value:-**Amount of maturity value = Principle Amount + Interest

Amount of maturity value = Rs. (640 × 54) + Rs. 9504

Amount of maturity value = Rs. 34,560 + Rs. 9504

Amount of maturity value = Rs. 44,064

**Question 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 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 :Calculation of A’s amount of recurring deposit:-**It is given that,

Deposit per month (P) = Rs. 1,200

Number of months (n) = 36

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

**Calculation of Simple Interest on Recurring Deposit:-**

**Calculation of maturity value:-**Amount of maturity value = Principle Amount + Interest

Amount of maturity value = Rs. (1200 × 36) + Rs. 6660

Amount of maturity value = Rs. 43,200 + Rs. 6660

Amount of maturity value = Rs. 49,860

**Calculation of B’s amount of recurring deposit:-**

Deposit per month (P) = Rs. 1,500

Number of months (n) = 30

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

**Calculation of Simple Interest on Recurring Deposit:-**

**Calculation of maturity value:-**Amount of maturity value = Principle Amount + Interest

Amount of maturity value = Rs. (1500 × 30) + Rs. 5812.50

Amount of maturity value = Rs. 45,000 + Rs. 5812.50

Amount of maturity value = Rs. 50,812.50

Difference between A’s Amount and B’s Amount = Rs. 50,812.50 – Rs. 49,860 = Rs. 952.50

**Hence, B will get more amount than A by Rs. 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 Rs. 12,715 as the maturity value of this account, what sum of money did money did he pay every month?** **Solution :**It is given that,

Deposit per month (P) = Rs. x

Number of months (n) = 12

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

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the amount of maturity is Rs. 12,715**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Rs. 12,715 = Rs.(x×12)+Rs.0.715x

Rs. 12,715 = Rs.12x+Rs.0.715x

Rs. 12,715 = Rs.12.715x

x=(Rs.12,715)/(Rs.12.715)

x=Rs.1,000

**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 Rs. 10,206 on maturity, find the value of monthly installments.** **Solution :**It is given that,

Deposit per month (P) = Rs.x

Number of months (n) = 42

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

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the amount of maturity is Rs. 10,206**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Rs. 10,206 = Rs.(x×42)+Rs.9.03x

Rs. 10,206 = Rs.42x+Rs.9.03x

Rs. 10,206 = Rs.51.03x

x=(Rs. 10,206)/(Rs. 51.03)

x=Rs.200

**Hence, the monthly installment of recurring deposit is Rs. 200.**

**Question 6. (i) Puneet has a Recurring Deposit Account in the Bank of Baroda and deposits Rs. 140 per month for 4 years. If he gets Rs. 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 Rs. 300 per month for two years. If he received Rs. 7,725 at the time of maturity, find the rate of interest per annum.**

**Solution :**

(i) It is given that,

Deposit per month (P) = Rs. 140

Number of months (n) = 48

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

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the amount of maturity is Rs. 8,092**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Rs. 8,092 = Rs.(140×48)+Rs.137.20x

Rs. 8,092 = Rs.6720+Rs.137.20x

Rs. 8,092 = Rs.6720+Rs.137.20x

Rs. 8,092 – Rs. 6720 = Rs.137.20x

Rs. 1372 = Rs.137.20x

x=(Rs. 1372)/(Rs. 137.20)

x=10%

**Hence, the Rate of interest is 10%.**

(ii)

It is given that,

Deposit per month (P) = Rs. 300

Number of months (n) = 24

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

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the amount of maturity is Rs. 7,725**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Rs. 7,725 = Rs.(300×24)+Rs.75x

Rs. 7,725 = Rs.7200+Rs.75x

Rs. 7,725 = Rs.7200+Rs.75x

Rs. 7,725 – Rs.7200 = Rs.75x

Rs. 525 = Rs.75x

x=(Rs. 525)/(Rs. 75)

x=7%

**Hence, the Rate of interest is 7%.**

**Question 7.Amit deposited Rs. 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 :**It is given that,

Deposit per month (P) = Rs. 150

Number of months (n) = 8

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

**Calculation of Simple Interest on Recurring Deposit:-**

Simple Interest = Rs. 36**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Amount of maturity value = Rs. (150 × 8) + Rs. 36

= Rs. 1200 + Rs. 36

= Rs. 1236

**Question 8. Mrs. Geeta deposited Rs. 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 Rs. 5,565; find the rate of interest per annum.** **Solution:**It is given that,

Deposit per month (P) = Rs. 350

Number of months (n) = 15

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

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the amount of maturity is Rs. 5,565**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Rs. 5,565 = Rs.(350×15)+Rs.35r

Rs. 5,565 = Rs.5250+Rs.35r

Rs. 5,565 = Rs.5250+Rs.35r

Rs. 5,565 – Rs.5250 = Rs.35r

Rs. 315 = Rs.35r

r=(Rs. 315)/(Rs. 35)

x=9%

**Hence, the Rate of interest is 9%.**

**Question 9. A recurring deposit account of Rs. 1,200 per month has a maturity value of Rs. 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 :**It is given that,

Deposit per month (P) = Rs. 1200

Number of months (n) = n

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

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the amount of maturity is Rs. 12,440**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Rs. 12,440 = Rs.(1200×n)+Rs.4n(n+1)

Rs. 12,440 = 1200n+4n

^{2}+4n

0 = 4n

^{2}+1204n-12440

4n

^{2}+1204n-12440 = 0

4(n

^{2}+301n-3110 =0

n

^{2}+301n-3110 = 0

n

^{2}+311n-10n-3110 = 0

n(n+311)-10(n+311) = 0

(n+311)(n-10) = 0

n=-311 or n =10 months

Months can’t be in negative hence the time is 10 months.

**Question 10. Mr. Gulati has a Recurring Deposit Account of Rs. 300 per month. If the rate of interest is 12% and the maturity value of this account is Rs. 8,100; find the time (in years) of this Recurring Deposit Account.** **Solution :**It is given that,

Deposit per month (P) = Rs. 300

Number of months (n) = n

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

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the amount of maturity is Rs. 8,100**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Rs. 8,100 = (300×n) + Rs.1.5n(n+1)

Rs. 8,100 = 300n+1.5n

^{2}+ 1.5n

0 = 1.5n

^{2}+ 301.5n – 8100

1.5(n

^{2}+ 201n – 5400) = 0

n

^{2}+ 201n – 5400 = 0

n

^{2}+ 225n – 24n-5400 = 0

n(n+225) – 24(n-225) = 0

(n+225)(n-24) = 0

n=-225 or n =24

Months can’t be in negative hence the time is 24 months.

**Question 11. Mr. Gupta opened a recurring deposit account in a bank. He deposited Rs. 2,500 per month for two years. At the time of maturity he got Rs. 67,500. Find:(i) the total interest earned by Mr. Gupta(ii) the rate of interest per annum.**

**Solution:**

(i)

It is given that,

Maturity value = Rs. 67,500

Money deposited per month = Rs. 2,500

Total Money deposited = Rs. 2,500 × 24

Total Money deposited = Rs. 60,000

Interest earned by Mr. Gupta = Rs. 67,500 – Rs. 60,000

Interest earned by Mr. Gupta = Rs. 7,500

**Hence, the Interest earned by Mr. Gupta is Rs. 7,500**

(ii)

It is given that,

Deposit per month (P) = Rs. 2,500

Number of months (n) = 24

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

**Calculation of Simple Interest on Recurring Deposit:-**

Interest earned = Rs. 7500

625r =7500

r=7500/625

r=12%**Hence, the rate of interest is 12%.**

### Exercise 2B

**Question 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:**It is given that,

Deposit per month (P) = Rs. 600

Number of months (n) = 48

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

**Calculation of Simple Interest on Recurring Deposit:-**

**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Amount of maturity value = Rs. (600 × 48) + Rs. 4,704

= Rs. 28,800 + Rs. 4704

= Rs. 33,504

**Question 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:**It is given that,

Deposit per month (P) = Rs. 80

Number of months (n) = 18 months

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

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the maturity value is Rs. 1,554**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Rs. 1,554 = Rs. (80 × 48) + Rs. 11.4r

Rs. 1,554 = Rs. 1,440 + Rs. 11.4r

Rs. 1,554 – Rs. 1,440 = Rs. 11.4r

114 = 11.4r

r = 114/11.4

r = 10%

**Hence, the rate of interest is 10%.**

**Question 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:**It is given that,

Deposit per month (P) =Rs. 400

Number of months (n) = n

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

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the amount of maturity is Rs. 16,176**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Rs. 16,176 = (400×n)+Rs. (4n(n+1))/3

Rs. 48,528 = 1200n+4n

^{2}+4n

Rs. 48,528 = 1204n+4n

^{2}

4n

^{2}+1204n-Rs.48,528 = 0

4(n

^{2}+301n-12132) = 0

n

^{2}+301n-12132=0

n

^{2}+337n-36n-12132 = 0

n(n+337)-36(n+337) = 0

(n+337)(n-36) = 0

n=-337 or n=36

**Months can’t be in negative hence the time is 36 months.**

**Q4. Mr. Bajaj needs Rs. 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 :**It is given that,

Number of months (n) = 24

Rate of interest = 8% p.a.

Let the Deposit per month (P) = Rs. P

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the amount of maturity is Rs. 30,000**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Rs. 30,000 = (P×24)+Rs.2P

Rs. 30,000 = 26P

P = 30,000/26

P = 1153.84

Principle will be in multiple of 5, hence money deposited by Mr. Bajaj is Rs. 1155.

**Question 5. Rishabh has recurring deposit account in a post office for 3 years at 8% p.a. simple interest. If he gets Rs. 9,990 as interest at the time of maturity, find:(i) The monthly installment.(ii) The amount of maturity.**

**Solution:**

It is given that,

Number of months (n) = 36

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

Let the Deposit per month (P) = Rs. P

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the interest is Rs. 9,990

4.44P = Rs. 9,990

P = Rs. 9,990/4.44

P = Rs. 2,250

**(ii) Calculation of Maturity value**Amount of maturity value = Principle Amount + Interest

Amount of maturity value = Rs.(2,250×36) + Rs.9,990

Amount of maturity value = Rs .(2,250×36) + Rs.9,990

Maturity value = Rs. 81,000 + Rs. 9,990

Maturity value = Rs. 90,990

**Question **6. Gopal has a cumulative deposit account and deposits Rs. 900 per month for a period of 4 years he gets Rs. 52,020 at the time of maturity, find the rate of interest.**Solution**:

It is given that,

Installment per month (P) = Rs. 900

Number of months (n) = 48

Let the rate of interest (r) = r% p.a. **Calculation of Simple Interest on Recurring Deposit:-**

It is given that the amount of maturity is Rs. 30,000**Calculation of amount of recurring deposit:-**Amount of maturity value = Principle Amount + Interest

Rs. 52,020 = (900×48)+Rs.882r

Rs. 52,020 = Rs. 43,200 + 882r

Rs. 52,020 – Rs. 43,200 = 882r

Rs. 8820 = 882r

r = Rs. 8820/882

P = 10%

Hence, the principle rate is 10%.

**Question **7. Deepa has a 4-year recurring deposit account in a bank and deposits Rs. 1,800 per month. If she gets Rs. 1,08,450 at the time of maturity, find the rate of interest.**Solution :**It is given that,

Installment per month (P) = Rs. 1,800

Number of months (n) = 48

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

**Calculation of Simple Interest on Recurring Deposit:-**

It is given that the amount of maturity is Rs. 1,08,450**Calculation of Maturity value:-**Amount of maturity value = Principle Amount + Interest

Amount of maturity value = Rs.(1800×48)+1764r

Rs. 1,08,450 = Rs.86,400+1,764r

Rs. 1,08,450 – Rs. 81,000 = 1,764r

1,764r = Rs. 1,08,450 – Rs. 81,000

1,764r = Rs. 22,050

r = Rs. 22,050/1,764

r = 12.5%

**Hence, the rate of interest is 12.5%.**

**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 installment.**Solution :**It is given that,

Rate of interest (r) = Rs. 8%

Number of months (n) = 12 × 3 = 36 months

Installment per month (P) = Rs. 900

**Calculation of Maturity Value:-**

8088 = 36P+P×4.44

8088 = 36P+4.44P

8088 = 40.44P

P = 8088/40.44

P = 200**Hence, the maturity value is the Rs. 200.**

**Question **9. Shahrukh opened a Recurring Deposit Account in a bank and deposited Rs. 800 per month for 1 1/2 years. If he received Rs. 15,084 at the time of maturity, find the rate of interest per annum.**Solution :**It is given that

Maturity Value (MV) = Rs. 15,084

Installment per month (P) = Rs. 800

Number of months (n) = 3/2×12 months = 18 months

**Calculation of Maturity Value:-**

Rs. 15,084 = Rs. 14,400 × 114r

Rs. 15,084 – Rs. 14,400 = 114r

Rs. 684 = 114r

114r = Rs. 684

r = Rs. 684/114

r = 6%**Hence, the rate of interest is 6%.**

**Question **10. 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 Rs. 1,000, find the:

(i) interest earned in 2 years

(ii) maturity value**Solution :**It is given that,

Installment per month (P) = Rs. 1000

Number of months (n) = 2year = 2 × 12month = 24 months

Rate of interest (r) = 6%

**Calculation of Simple Interest:-**

Simple Interest = Rs.1500**Hence, the interest in 2years is Rs. 1500.**

(ii) Total money deposited = Rs. 1000 × 24

Total money deposited = Rs. 24,000

Maturity Value = Money deposited + Interest

Maturity Value = 24,000 + 1,500

Maturity Value = Rs. 25,500**Hence, the maturity value is Rs. 25,500.**

**Question **11. Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs. 1200 as interest at the time of maturity, find

(i) the monthly installment

(ii) the amount of maturity**Solution :**It is given that,

Amount of interest (i) = Rs. 1,200

Number of months (n) = 2 years = 2 × 12 = 24 months

Rate of interest (r) = 6%

**(i) Calculation of Monthly installment:-**

**Hence, the monthly interest is Rs. 800.**

(ii) Calculation of amount of maturity:-

Total sum deposited = P × n = Rs. 800 × 24 = Rs. 19,200

Amount of maturity = Total sum deposited + Interest on it

Amount of maturity = Rs. (19,200 + 1,200)

Amount of maturity = Rs. 20,400

Hence, the maturity amount is Rs. 20,400

**Question **12. Peter has a recurring deposit account in Punjab National Bank at Sadar Bazar, Delhi for 4 years at 10% p.a. He will get Rs. 6,370 as interest on maturity. Find:

(i) monthly installment,

(ii) the maturity value of the account.**Solution :**It is given that,

Rate of interest (r) = 10%

Number of month (n) = 4 years = 4 × 12 = 48 months

Interest = Rs. 6370

Let the Installment per month (P) = P

**Hence, the monthly installment is Rs. 650**

(ii) Calculation of amount of maturity:-

Amount of maturity = Total sum deposited + Interest on it

Amount of maturity = Rs.31,200 + Rs. 6370

Amount of maturity = Rs. 37,570**Hence, the maturity amount is Rs. 37,570**