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Mathematics [4 marks sum]

Banking · ICSE STD 10 (ICSE - English Medium). 18 questions.

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[4 marks sum]

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18 questions · timed · auto-graded

Question 14 Marks
Ms. Saha opened a cumulative deposit account of monthly instalment of Rs $1,200$ at $9\%$ p.a simple interest. She earned a total interest of Rs $5,328.$ How much installments did she pay?
Answer
Given that, cumulative deposit per month $=$ Rs $1200 ,$ Period $=t$ Months, $R=9 \%$, Interest amount= Rs. $5328$
Money deposited $=$ Monthly value $x$ No ofMonths $=1200 x$ t $=$ Rs $1200 t$
Total Principal for 1 Month $=\frac{1200 \times( t )( t +1)}{2}$
$=600 t^2+600 t$
$\text { Interest }=\frac{\text { Principal for One month } \times R }{12 \times 100}\ldots (1)$
Putting Values in (1), we get
$ 5328=\frac{\left(600 t^2+600 t\right) \times 9}{1200}$
$\Rightarrow 5328=\left(4.5 t^2+4.5 t\right)$
$\Rightarrow 4.5 t^2+4.5 t-5328=0$
$\Rightarrow t=34 \text { months (approximately) } $
Thus, she paid $34$ installments.
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Question 24 Marks
Mr. Banerjee opens a recurring deposit account for Rs 3,000 per month at 9% simple interest pa. On maturity, he gets Rs. 1,70,460. Find the period for which he continued with the account.
Answer
Given that cumulative deposit per month $= Rs 3000$, Period $= t$ Months, $R =9 \%$, Maturity amount= Rs. $1,70,460$
Money deposited $=$ Monthly value $\times$ No ofMonths $=3000 \times t=$ Rs $3000 t$
Total Principal for 1 Month $=\frac{3000 \times( t )( t +1)}{2}$
$=1500 t^2+1500 t$
Interest= Principal for One month $\times RI (12 \times 100)$$\ldots(1)$
Putting Values in (1), we get
$ 170460-3000 t=\frac{\left(1500 t^2+1500 t\right) \times 9}{1200}$
$170460-3000 t=\frac{45 t^2+45 t}{4}$
$45 t^2+12045 t-681840=0$
$45 t^2-2160 t+14205 t-681840=0$
$45 t(t-48)+14205(t-48)=0$
$(t-48)(45 t+14205)=0$
$t=48, t=-\frac{14205}{45} $
The number of months cannot be negative.
Hence, $t =48$ months $=4$ years
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Question 34 Marks
Mr. Mohan has a cumulative deposit account for 3 years at 7% interest pa. She receives Rs 8,547 as a maturity amount after 3 years.
(a) Find the monthly deposit.
(b) Find the total interest receivable after maturity.
Answer
Given that cumulative deposit per month $= P$, Period $=3$ years $=36$ Months, $R =7 \%$, Maturity amount $=$ Rs 8,547
Money deposited $=$ Monthly value $\times$ No of Months $= P \times 36=$ Rs $36 P$
Total Principal for 1 Month $=$ Rs $\frac{ P \times(36)(36+1)}{2}=$ Rs $666 P$
Interest= Principal for One month $\times R /(12 \times 100)$..... (1)
Putting Values in (1), we get
Rs $8547-36 P =\frac{666 P \times 7}{12 \times 100}$
$8547-36 P =3.885 P$
$\Rightarrow P = Rs 214.3$
Interest amount $=8547-36 P$
$=$ Rs 832 Interest amount $=832$
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Question 44 Marks
Aarushi has a recurring deposit account for $2$ years at $6\%$ pa. She receives Rs $1,125$ as interest on maturity.
(a) Find the monthly instalment amount.
(b) Find the maturity amount.
Answer
Given that Recurring deposit per month $= P$, Period $=2$ years $=24$ Months, $R =6 \%$, Interest amount = Rs $1, 125$
Money deposited $=$ Monthly value $\times$ No of Months $= P \times 24= Rs 24 P$
Total Principal for $1$ Month $=$ Rs $\frac{ P \times(24)(24+1)}{2}=$ Rs $300 P$
Interest= Principal for One month $x$ RI $(12 \times 100)\ldots(1)$
Putting Values in (1), we get
$ \text { Rs } 1125=\frac{300 P \times 6}{12 \times 100}$
$P=\text { Rs } \frac{1125 \times 12 \times 100}{300 \times 6}$
$P=\text { Rs } 750$
$\text { Maturity amount }=P \times 24+\text { Interest }$
$=750 \times 24+1125$
$\Rightarrow \text { Maturity amount }=19,125 $
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Question 54 Marks
Mr. Menon deposit Rs 1,200 per month in a cumulative deposit account for a period of 5 years. After the end of the period, he will receive Rs 88,470. (a) Find the rate of the interest per annum. (b) Find the total interest that Mr. Menon will earn.
Answer
Given that Recurring deposit per month $=$ Rs 1,200 , Period $=5$ years $=60$
Months, R=R0/o, Maturity value $= Rs 88,470$ Money deposited $=$ Monthly value $x$ No of Months $=1,200 \times 60=$ Rs 72,000
$\Rightarrow$ Interest that gets for this period = Maturity Value - Amount deposited
$=\operatorname{Rs}(88,470-72,000)$
$=\operatorname{Rs} 16,470$
Total Principal for 1 Month $=$ Rs $\frac{1200 \times(60)(60+1)}{2}=$ Rs 2196000
Rs $16470=\frac{ R \times 2196000}{12 \times 100}$
$\Rightarrow R =\frac{16470 \times 12 \times 100}{2196000}$
$R=9 \%$
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Question 64 Marks
Mr. Patel deposit Rs 2,250 per month in a recurring deposit account for a period of 3 years. At the time of maturity, he gets Rs 90,990.
(a) Find the rate of simple interest per annum.
(b) Find the total interest earned by Mr. Patel.
Answer
Given that Recurring deposit per month $=$ Rs 2,250, Period $=3$ years $=36$
Months, R=R0/o, Maturity value $= Rs 90,990$
Money deposited $=$ Monthly value $x$ No of Months
$
=2,250 \times 36=\operatorname{Rs} 81,000
$
$\Rightarrow$ Interest that gets for this period $=$ Maturity Value - Amount deposited $=90,990-81,000$
$
=\text { Rs } 9,990
$
Total Principal for 1 Month $=$ Rs $\frac{2250 \times(36)(36+1)}{2}=$ Rs 1498500
$
9990=\frac{ R \times 1498500}{12 \times 100}
$
$
\Rightarrow R =\frac{9990 \times 12 \times 100}{1498500}
$
$
R=8 \%
$
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Question 74 Marks
Mrs Khandelkar invests Rs 900 every month in a recurring deposit account for a period of 3 years at a simple interest rate of 8% pa
(a) Find the total interest she will earn at the end of the period.
(b) Find the maturity value of her deposits.
Answer
Given that Recurring deposit per month $=$ Rs 900 , Period $=3$ years $=36$ Months, $R=8 \%$
Money deposited $=$ Monthly value $✗$ No of Months
$
=900 \times 36=\text { Rs } 32,400 \text {.$\ldots (1)$ }
$
Total Principal for 1 Month=Rs $\frac{900 \times(36)(36+1)}{2}=$ Rs 599400
Interest $=$ Rs $\frac{8 \times 599400}{12 \times 100}=$ Rs 3996$\ldots (2)$
Hence Maturity Amount $=(1)+(2)$
$
=\operatorname{Rs}(32,400+3,996)
$
Hence Maturity Amount= Rs 36,396
And Interest= Rs 3,996
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Question 84 Marks
Mrs. Chhabra deposits Rs 500 per month in a recurring deposit account for 4 years at a simple interest rate of 6% pa.
(a) Find the maturity value of deposit.
(b) Find the total interest she will earn after 2 years
Answer
Given that recurring deposit per month $=$ Rs 500, Period $=4$ years $=48$ Months, $R=6 \%$
Money deposited $=$ Monthly value $✗$ No of Months
$
=500 \times 48=\operatorname{Rs} 24,000\ldots (1)
$
Total Principal for 1 Month= Rs $\frac{500 \times(48)(48+1)}{2}=$ Rs 588000
$
\text { Interest }=\text { Rs } \frac{6 \times 588000}{12 \times 100}=\text { Rs } 2940\ldots (2)
$
Hence Maturity Amount $=(1)+(2)$
$
=\operatorname{Rs}(24,000+2,940)
$
Hence Maturity Amount= Rs 26,940
And Interest $=$ Rs 2,940
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Question 94 Marks
Given below is a page from the passbook of a saving bank account that Mr. Sharma has with SBI. If the bank gives interest at 6%pa, find
The principal amount in January, February and March which will be considered for interest for interest calculation.
Answer
DateParticularsWithdrawalsDepositsBalanceQualifying amount
05.01.2008By Cash 15500.0015500.0015500.00
10.01.2008To Cheque4800.00 10700.0010700.00
15.02.2008To Cheque5300.00 5400.005400.00
08.03.2008By Cash 19200.0024600.0024600.00
17.03.2008By Cheque 7400.0032000.0024600.00
January: Rs. 10,700.00/- as this is minimum of 10th and 31st Jan
February: Rs. 5,400.00/- as this is minimum of 10th and 28th Feb
March: Rs. 24,600.00/- as this is minimum of 10th and 31st March (including 17th March)
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Question 104 Marks
Ms. Chitra opened a saving bank account with SBI on 05.04.2007 with a cheque deposit of Rs 11,000/.Subsequently, she took out Rs 3,200/- on 12.05.2007; deposited a cheque of Rs. 8,800/- on 03.06.2007 and paid Rs 2,000/- by cheque on 18.06.2007.
Make the entries in her passbook.
Answer
Make the entries in her passbook
DateParticularWithdrawalsDepositsBalance
05.04.2007By Cheque 11000.0011000.00
12.05.2007To Self3200.00 7800.00
03.06.2007By Cheque 8800.0016600.00
18.06.2007To Cheque2000.00 14600.00
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Question 114 Marks
Mr. Punjwanis saving account passbook had the following entries, The bank pays interest at 4.5°/o on all SB accounts. Find the amount received by Mr. Punjwani when he closed the acoount on 2S'h July 08.
DateParticularsWithdrawlsDepositsBalance
05.01.2008By B/F 24650.00
09.01.2008By cash 14390.0039040.00
15.02.2008To Cheque7600.00 31440.00
21.02.2008By Cheque 8350.0039790.00
07.03.2008To Cash4000.00 35790.00
31.03.2008By Interest
08.04.2008By Cheque 13670.00
12.04.2008To Cash6000.00
01.05.200By Cheque 17350.00
16.06.2008By Cash 9000.00
27.06.2008To Cash4370.00
04.07.2008By Cheque 21320.00
11.07.2008To Cheque9460.00 c
Answer
MonthsMinimum balance between 10th day and the last day
Jan39040
Feb31440
Mar35790
Principal at the end of march =Rs 106270
$
\text { Interest }=\frac{106270 \times 4.5 \times 1}{100 \times 12}=398.51
$
So the interest is Rs 399
After substituting th is interest the pass book is as follows:
DateParticularsWithdrawlsDepositsBalance
05.01.2008By B/F 24650.00
09.01.2008By cash 14390.0039040.00
15.02.2008To Cheque7600.00 31440.00
21.02.2008By Cheque 8350.0039790.00
07.03.2008To Cash4000.00 35790.00
31.03.2008By Interest 399.0036189.00
08.04.2008By Cheque 13670.0049859.00
12.04.2008To Cash6000.00 43859.00
01.05.200By Cheque 17350.0061209.00
16.06.2008By Cash 9000.0070209.00
27.06.2008To Cash4370.00 65839.00
04.07.2008By Cheque 21320.0087159.00
11.07.2008To Cheque9460.00 77699.00
Net Money that Mr. Punjwani will get is Rs 77,699/-.
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Question 124 Marks
The following enb·ies are from the saving bank account passbook of Mr. Ratnesh. If the rate of interest paid by the bank is 4. 5°/op.a. calculated at the end of March and September, find the balance in his account at the end of the year.
DateParticularsWithdrawlsDepositsBalance
03.01.2006By B/F 17900.00
09.01.2006To Cash3700.00 14200.00
06.02.2006To Cheque2450.00 11750.00
21.02.2006By Cash 15600.0027350.00
17.03.2006By Cash 9850.0037200.00
31.03.2006By Interest
06.06.2006To Cheque4100.00
22.08.2006To Cash1500.00
05.09.2006By Cheque 17300.00
09.09.2006To Cash6300.00
30.09.2006By Interest
04.12.2006To Cash3000.00
11.12.2006By Cheque 11760.00
Answer
MonthsMinimum balance between 10th day and the last day
Jan14200
Feb11750
Mar27350
Total principal at the end of March $=\operatorname{Rs} 53,300$
Interest at the end of March
$
=\frac{53300 \times 4.5 \times 1}{100 \times 12}=199.87
$
Thus the interest is Rs 200 Now entering the interest in pass book we get the remaining balances as below:
DateParticularsWithdrawlsDepositsBalance
03.01.2006By B/F 17900.00
09.01.2006To Cash3700.00 14200.00
06.02.2006To Cheque2450.00 11750.00
21.02.2006By Cash 15600.0027350.00
17.03.2006By Cash 9850.0037200.00
31.03.2006By Interest 200.0037400.00
06.06.2006To Cheque4100.00 33300.00
22.08.2006To Cash1500.00 31800.00
05.09.2006By Cheque 17300.0049100.00
09.09.2006To Cash6300.00 42800.00
30.09.2006By Interest 810.0043610.00
04.12.2006To Cash3000.00 40610.00
11.12.2006By Cheque 11760.0052370.00
* Interest calculated below.For calculating interest at the end of September.
MonthsMinimum balance between 10th day and the last day
Apr37400
May37400
June33300
July33300
Aug31800
Sep42800
Total principal at the end of September= Rs 216000
$
\text { Interest }=\frac{216000 \times 4.5 \times 1}{100 \times 12}=810
$
Now entering the interest in the pass book above, we get the balance Rs 52,370 at the end o year.
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Question 134 Marks
The following are the entries in the passbook of a saving account of Ananya during the year 2007. If interest is calculated at 5 % pa, find the interest earned by Ananya during the year
DateParticularsWithdrawalsDepositsBalance
01.01.2007By B/F 6500.00
05.02.2007By Cheque 7500.0014000.00
09.02.2007To Cash1500.00 12500.00
06.06.2007By Cash 1725.0014225.00
08.09.2007By Cheque 375.0014600.00
06.11.2007By Cash 6000.0020600.00
10.12.2007To Cheque2500.00 18100.00
Answer
MonthsMinimum balance between 10th day and the last day
Jan6500
Feb12500
Mar12500
Apr12500
May12500
June14225
July14225
Aug14225
Sep14600
Oct14600
Nov20600
Dec18100
Principal at the end of Dec. $=$ Rs $1,67,075$
$
\text { Interest }=\frac{167075 \times 5 \times 1}{100 \times 12}=696.14
$
Thus, interest is Rs 696.
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Question 144 Marks
Given below is a page from the passbook of a saving bank account of Dolly Majumdar. Complete the entries in the passbook and find the interest earned by the account holder in the month of November if the rate of simple interest is 5°/o pa. 
DateParticularWithdrawalsDepositsBalance 
01.04.2007By B/F  16500.00
15.04.2007By Cash  2500.00 
09.06.2007To Cheque6500.00  
04.07.2007By Cash  9000.00 
12.07.2007To Cash 3500.00  
05.09.2007To Cash 4000.00  
10.11.2007By Cheque 12000.00 
Answer
Balance =Previous Balance +Deposit - Withdrawal. Using this formula, we get following values in Balance column
DateParticularsWithdrawalsDepositsBalance
01.04.2007By B/F 16500.00
15.04.2007By Cash 2500.0019000.00
09.06.2007To Cheque6500.00 12500.00
04.07.2007By Cash 9000.0021500.00
12.07.2007To Cash3500.00 18000.00
05.09.2007To Cash4000.00 14000.00
10.11.2007 By Cheque 12000.0026000.00
Interest earned by account holder 1n the month of November
MonthsMinimum balance between 10th day and the last day
Apr16500
May19000
June12500
July18000
Aug18000
Sep14000
Oct14000
Nov26000
Total principal at the end of Nov $=\operatorname{Rs} 1,38,000$
$
\text { Interest }=\frac{138000 \times 5 \times 1}{100 \times 12}=575
$
Hence the interest earned is Rs 575 .
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Question 154 Marks
Given below is a page from the passbook of the savings bank account of Mr. Rajesh. Complete the entries in the passbook and calculate the interest paid to him by the bank at 6°/o pa in the end of June.
DateParticularsWithdrawalsDepositsBalance
08.02.2008 By Cash 12000.00
15.03.2008 To cash 3000.00
08.04.2008 To Cheque 2500.00
18.04.2008 By Cash 16000.00
10.06.2008 By Cash 800.00
Answer
DateParticularsWithdrawalsDepositsBalance
08.02.2008By Cash 12000.0012000.00
15.03.2008To cash3000.00 9000.00
08.04.2008To Cheque2500.00 6500.00
18.04.2008By Cash 16000.0022500.00
10.06.2008By Cash 800.0030500.00

MonthsMinimum balance between 10th day and the last day
Feb.12000
Mar.9000
Apr.6500
May22500
June30500

Total Principal at the end of June $=$ R.s 80,500
$
\text { Interest }=\frac{80500 \times 6 \times 1}{100 \times 12}=402.50 \text { (Rs } 4.3 \text { approx.) }
$
Hence, Mr. R.ajesh will get R.s 403/- as interest amount towards the end of June 2008.
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Question 164 Marks
Ms. Chitra opened a saving bank account with SBI on 05.04.2007 with a cheque deposit of Rs 11,000/.Subsequently, she took out Rs 3,200/- on 12.05.2007; deposited a cheque of Rs. 8,800/- on 03.06.2007 and paid Rs 2,000/- by cheque on 18.06.2007.
If the rate of simple interest was 5% pa compounded at the end of March and September, find her balance on 1.04.2008.
Answer
If the rate of simple interest was $5 \%$ pa compounded at the end of March and September, find her balance on 1.04.2008 According to the entries in passbook, the minimum balance tor ditterent months are as follows:
MonthsMinimum balance between 10th day and the last day Minimum balance in nearest multiple of 10
2007,April1100011000
May78007800
June1460014600
July1460014600
August1460014600
September1460014600
October14600 + 322 = 1492214920
November1492214920
December1492214920
2008,January1492214920
February1492214920
March1492214920

Total principal at the end of September 2007
=Rs $11000+7800+14600 \times 4$
=Rs 77200
Therefore interest at the end of sep. 2007
$
=\frac{77200 \times 5 \times 1}{100 \times 12}=321.66
$
Thus interest earned is Rs 322
Again, principal at the end of March, $2008=14920 \times 6=89520$
Therefore interest at the end of Mar. 2008
$
=\frac{89520 \times 5 \times 1}{100 \times 12}=373
$
Hence, Account balance as on 01.04.2008 is
$=$ Rs $14920+$ Rs 373
=Rs 15293
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Question 174 Marks
Mr. Burman open a saving back account with Bank of India on $3^{rd}$ April $2007$ with a cash deposit of $Rs. 5,000/-$. Subsequently, he deposited $Rs. 16,500/-$ by cheque on $11^{th}$ April $2007$, withdraw $Rs. 4,000/-$ on $10^{th}$ May, paid $Rs. 3,500$ for insurance by cheque on $7^{th}$ July $200,7$ deposited $Rs. 6,000/-$ in cash on $9^{th}$ August $2007$ and withdrew $Rs. 1,500/-$ on $12^{th}$ Oct $2007.$ If he closed the account on $14^{th}$ December and if the rate of simple interest is $4\%$ pa, then find the amount he received on closing the account.
Answer
If he closed the acoount on $14^{th}$ December and if the rate of simple interest is $4 \%$ pa, then find the amount he received on closing the account. Pis. note that there are June, September and November month where no transactions were made but the bank will give interest based on the amount which is reflected in the last month.
Months Minimum balance between $10^{th}$ day and the last day
Apr $5000$
May $17500$
June $17500$
July $14000$
Aug $20000$
Sep $20000$
Oct $18500$
Nov $18500$
Total principal for at the end of November $=1,31,000$
$\text { Interest }=\frac{131000 \times 4 \times 1}{100 \times 12}=436.67$
Thus, interest$= Rs. 437$
Hence, while closing the account, Mr. Burman will get Principal $+$ interest which amounts to$:$
$Rs. 18,500/- + Rs. 437/- = Rs. 18, 937/-$
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Question 184 Marks
Mr. Burman open a saving back account with Bank of India on $3^{rd}$ April $2007$ with a cash deposit of $Rs. 5,000/-$. Subsequently, he deposited $Rs. 16,500/-$ by cheque on $11^{th}$ April $2007,$ withdraw $Rs. 4,000/-$ on $10^{th}$ May, paid $Rs. 3,500$ for insurance by cheque on $7^{th}$ July $2007,$ deposited $Rs. 6,000/-$ in cash on $9^{th}$ August $2007$ and withdrew $Rs. 1,500/- $ on $12^{th}$ Oct $2007.$ Make the entries in his passbook.
Answer
Make the entries in his passbook There are $5$ columns in a passbook:
$a)$ Date,
$b)$ Particulars,
$c)$ Withdrawals,
$d)$ Deposits,
$e)$ Balance.
Date is the date of the transaction, Particular is the details of the transaction primarily the name, Withdrawal is the amount that has been taken out from acoount, Deposit is the amount that has been given to the acoount, balance is net amount remaining in the account after subtracting I Adding the amount as applicable. Keeping this in mind, the passbook entry will look as below:
Date Particular Withdrawals Deposits Balance
$03.04.2007$ By cash   $5,000.00$ $5,000.00$
$11.04.2007$ By Cheque   $16,500.00$ $21,500.00$
$10.05.2007$ To Self $4,000.00$   $17,500.00$
$07.07.2007$ By Cheque $3,500.00$   $14,000.00$
$09.08.2007$ By cash   $6,000.00$ $20,000.00$
$12.10.2007$ To Self $1,500.00$   $18,500.00$
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