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+4n2+4n
0 = 4n2+1204n-12440
4n2+1204n-12440 = 0
4(n2+301n-3110 =0
n2+301n-3110 = 0
n2+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+1.5n2 + 1.5n
0 = 1.5n2 + 301.5n – 8100
1.5(n2 + 201n – 5400) = 0
n2 + 201n – 5400 = 0
n2 + 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+4n2+4n
Rs. 48,528 = 1204n+4n2
4n2+1204n-Rs.48,528 = 0
4(n2+301n-12132) = 0
n2+301n-12132=0
n2+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
