Question

A man has a Recurring Deposit Account in a
bank for 3.5 years. If the rate of interest is
12% per annum and the man gets 10,206
on maturity, find the value of monthly
instalments.​

Answer 1

Step-by-step explanation:

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Answer 2

$\underline{ \underline{{ \huge{ \mathtt{Q}}} \mathtt{UESTION -}}}$

A man has a recurring deposit account in a bank for 3.5 years. If the rate of interest is 12% per annum and the man gets ₹ 10,206 on maturity, find the value of monthly ins.tallments.

$\underline{ \underline{{ \huge{ \mathtt{G}}} \mathtt{IVEN -}}}$

• number of months (n) = 3.5 = 3½ years to months

$\mathtt{ 3 \frac{1}{2} = \frac{7}{2} \times 12 \implies \: 42 \: months }$

• Rate of interest (r) = 12%
• Maturity value (M.V) = ₹ 10,206

$\underline{ \underline{{ \huge{ \mathtt{T}}} \mathtt{O } \: \: \: {{ \huge{ \mathtt{F}}} \mathtt{IND -}}}}$

• Value of monthly ins.tallments (principal amount).

$\underline{ \underline{{ \huge{ \mathtt{F}}} \mathtt{ ORMULA } \: \: \: {{ \huge{ \mathtt{U}}} \mathtt{SED -}}}}$

$\underline{ \boxed{ \gray{ \mathtt{M.V = P \times n + \frac{P \times n(n + 1)}{2 \times 12} \times \frac{r}{100} }} }}$

where,

M .V is the maturity value.

P is the principal.

n is the number of months.

r is the rate of interest.

$\underline{ \underline{{ \huge{ \mathtt{S}}} \mathtt{OLUTION -}}}$

$\mathtt{M.V = P \times n + \frac{P \times n(n + 1)}{2 \times 12} \times \frac{r}{100} } \\ \\ \mathtt{ \implies{₹ \: 10,206 =P \times 42 + \frac{P \times 42(42 + 1)}{2 \times 12} \times \frac{12}{100} }} \\ \\ \mathtt{ \implies{10206 = P \times 42 + \frac{P \times 42 \times 43}{2 \times 12} \times \frac{12}{100} }} \\ \\ \mathtt{ \implies{10206 = 42 \: P + \frac{P \times \cancel{42} ^{21} \times 43}{ \cancel2 \times \cancel{12}} \times \frac{ \cancel{12}}{100} }} \\ \\ \mathtt{ \implies{10206 = 42 \: P + \frac{903 \:P }{100} }} \\ \\ \mathtt{ \implies{10206 = \frac{4200 \: P + 903 \: P}{100} }} \\ \\ \mathtt{ \implies{10206 = \frac{5103 \: P}{100} }} \\ \\ \mathtt{ \implies{ \frac{ \cancel{10206} ^{2} \times 100}{ \cancel{5103}} = P}} \\ \\ \boxed{ \purple{ \mathtt{ \therefore{P = ₹ \: 200 \: \: \: ans.}}}}$

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@MissSolitary✌️

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