Question

The simple interest on a sum of money for 2 years at 6½ % per annum is rs 5200. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?

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Answer 1

Answer:

Compound Interest = Rs. 5369

Step-by-step explanation:

SI = Rs. 5200

N = 2 years

R = 6.5 p.c.p.a

$i \: = \frac{p \times n \times r}{100}$

$5200 = \frac{p \times 2 \times 6.5}{100}$

$\frac{5200 \times 100}{2 \times 6.5} = p$

$40000 = p$

P = Rs. 40000

$a \: = p \times (1 + \frac{r}{100} )$

a = amount at the end of 2 years, if compounded annually

$a \: = 40000 \times ( 1 + \frac{6.5}{100} ) ^{2}$

$a \: = 40000 \times ( \frac{100 + 6.5}{100} ) ^{2}$

$a \: = 40000 \times ( \frac{106.5}{100} ) ^{2}$

$a \: = 40000 \times \frac{106.5}{100} \times \frac{106.5}{100}$

a = Rs. 45369

CI = a - p

= 45369 - 40000

CI = Rs. 5369

I hope it helps...

Answer 2

✤ Your Query ✤

The simple interest on a sum of money for 2 years at 6½ % per annum is rs 5200. What will be the compound interest on the same sum at the same rate for the same period, compounded annually?

✤ Required Answer ✤

• Simple interest = rs 5200

• Rate = 6½ % p.a = 13/2 % p.a

• Time = 2 years

$\begin{gathered} \\ : \implies \displaystyle \sf \: Sum(P) = \dfrac{100 \times SI }{R \times T } \\ \\ \\ \end{gathered}$

$\begin{gathered} \\ : \implies \displaystyle \sf \: Sum(P) = rs \: \dfrac{100 \times 5200 }{ \dfrac{13}{2} \times 2 } = rs \: 40000 \\ \\ \\ \end{gathered}$

Now ,

• Principal = rs 40000

• Rate = 6½ % p.a

• Time = n = 2 years

$\begin{gathered} \\ \\ : \implies \displaystyle \sf \: A = P \bigg(1 + \dfrac{R}{100}\bigg)^{n} \\ \\ \\ \end{gathered}$

Amount after two years

$\begin{gathered} \\ \\ : \implies \displaystyle \sf \: rs \Bigg[ 40000\bigg(1 + \dfrac{ \dfrac{13}{2} }{100}\bigg)^{2} \Bigg] \\ \\ \\ \end{gathered}$

$\begin{gathered} \\ \\ : \implies \displaystyle \sf \: rs \Bigg[ 40000\bigg(1 + \dfrac{ 13}{200}\bigg)^{2} \Bigg] \\ \\ \\ \end{gathered}$

$\begin{gathered} \\ \\ : \implies \displaystyle \sf \: rs \Bigg[ 40000\bigg(\dfrac{ 213}{200}\bigg)^{2} \Bigg] \\ \\ \\ \end{gathered}$

$\begin{gathered} \\ \\ : \implies \displaystyle \sf \: rs \Bigg[ 40000\times \dfrac { 213}{200} \times \dfrac{ 213}{200}\ \Bigg] \\ \\ \\ \end{gathered}$

$\begin{gathered} \\ \\ : \implies \displaystyle \sf \: rs \: 45369 \\ \\ \\ \end{gathered}$

Compound Interest = Amount - Principal

= rs ( 45369 - 40000 )

= rs 5369

$\begin{gathered}: \implies \underline{ \boxed{ \displaystyle \sf \: rs \: 5369 }} \\ \\ \end{gathered}$

$\begin{gathered}: \implies \underline{ \boxed{ \displaystyle \sf \: Hence , \: the \: compound \: interest \: is \: rs \: 5369 }} \\ \\ \end{gathered}$

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✤ Additional Information ✤

Compound Interest ( CI )

• Financial institutions, insurance companies, post offices, banks and other companies which lend money and accept deposits follow an entirely different procedure for calculating interest.

• Here, the borrower and lender fix a certain unit of time to work out the interest.

• The principal changes after each fixed unit of time because the interest accrued during the fixed unit of time is added to the principal and the amount obtained is considered as the principal for the next unit of time.

• The interest for the next unit of time is computed on this new principal and so on.

• After a certain specified period the difference between the amount and the money borrowed is calculated and this difference is called the compound interest (CI).

• The fixed unit of time is called the conversion period.