[2 Mark Question Answer]

Question 12 Marks

Sharukh opened a recurring deposit account in a bank and deposited $Rs.800$ per month for $1 \frac{1}{2}$ years. If he recieved $Rs.15,084$ at the time of maturity, find the rate of interest per annum

Answer

Monthly deposit (P) $= Rs.800$
$n =\frac{3}{2} \times 12 \text { months }=18 \text { months }$
Maturity value (M.V) $= Rs.15084$
Now, M.V $=P \times N+P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}$
$\Rightarrow 15084=800 \times 18+800 \times \frac{18 \times 19}{24} \times \frac{r}{100} $
$ \Rightarrow 15084=14400+114 r $
$ \Rightarrow 114 r=684 $
$\Rightarrow r=\frac{684}{114}=6 \%$
Thus, the rate of interest per anum is $6\%.$

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Question 22 Marks

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.

Answer

Installment per month(P) $= Rs.600$
Number of months(n) $= 48$
Rate of interest(r) $= 8\%$ p.a
$\therefore \text { S.I }= P \times \frac{ n ( n +1)}{2 \times 12} \times \frac{ r }{100} $
$ =600 \times \frac{48(48+1)}{2 \times 12} \times \frac{8}{100} $
$ =600 \times \frac{2352}{24} \times \frac{8}{100}=\operatorname{Rs} 4704$
The amount that Manish will get at the time of maturity
$= Rs.(600 × 48) + Rs.4,704$
$= Rs.28,800 + Rs.4,704$
$= Rs.33,504$

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Question 32 Marks

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?

Answer

Installment per month(P) $= Rs.150$
Number of months(n) $= 8$
Rate of interest(r) $= 8\%$ p.a.
$\therefore S . I = P \times \frac{ n ( n +1)}{2 \times 12} \times \frac{ r }{100}$
$=150 \times \frac{8(8+1)}{2 \times 12} \times \frac{8}{100} $
$ =150 \times \frac{72}{24} \times \frac{8}{100}=\text { Rs } 36$
The amount that Manish will get at the time of maturity
$= Rs.(150 × 8) + Rs.36$
$= Rs.1,200 + Rs.36$
$= Rs.1,236$

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Question 42 Marks

Mrs Mathew opened a Recurring Deposit Account in a certain bank and deposited $₹ 640$ per month for $4^{1/2}$ years. Find the maturity value of this account, if the bank pays interest at the rate of $12\%$ per year.

Answer

Installment per month(P) $= Rs.640$
Number of months(n) $= 54$
Rate of interest(r) $= 12\%$ p.a.
$\therefore S . I = P \times \frac{ n ( n +1)}{2 \times 12} \times \frac{ r }{100}$
$=640 \times \frac{54(54+1)}{2 \times 12} \times \frac{12}{100}$
$=640 \times \frac{2970}{24} \times \frac{12}{100}=\operatorname{Rs} 9504$
The amount that Manish will get at the time of maturity
$=\operatorname{Rs}(640 \times 54)+\operatorname{Rs} 9504 $
$ =\operatorname{Rs} 34560+\operatorname{Rs} 9504 $
$ =\text { Rs } 44064$

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Question 52 Marks

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.

Answer

Installment per month(P) = Rs 600
Number of months(n) = 20
Rate of interest(r) = 10% p.a.
$\therefore S . I = P \times \frac{ n ( n +1)}{2 \times 12} \times \frac{ r }{100}$
$=600 \times \frac{20(20+1)}{2 \times 12} \times \frac{10}{100}$
$=600 \times \frac{420}{24} \times \frac{10}{100}=\operatorname{Rs} 1050$
The amount that Manish will get at the time of maturity
= Rs (600 × 20) + Rs 1050
= Rs 12000 + Rs 1050
= Rs 13050

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Question 62 Marks

Mr. Gupta opened a recurring deposit account in a bank. He deposited Rs. 2500 per month for two years. At the time of maturity he got Rs. 67,500. Find:1) the total interest earned by Mr Gupta.
2) the rate of interest per annum.

Answer

1) Monthly instalment $= Rs. 2500$
$n = 24,$ Amount deposited $= 2500 \times 24 = Rs. 60000$
Maturity value $= Rs. 67500$
Interest on his deposit $= Rs. (67500 – 60000) = Rs. 7500$

2) Now Interest $=\frac{ n ( n +1)}{2} \times \frac{\text { Instalment } \times \text { Rate }}{100 \times 12}$
$7500=\frac{24 \times 25}{2} \times \frac{2500 \times \text { Rate }}{100 \times 12}$
$\text { Rate }=\frac{7500 \times 100 \times 24}{24 \times 25 \times 2500}=12 \% \text { p.a }$

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Mathematics [2 Mark Question Answer]

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