Math, asked by NightSparkle, 20 hours ago

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Kamala borrowed Rs.26,400 from a Bank to Bye a Scooter bat a rate of 15% p.a. Compounded Yearly .What amount will she pay at the end of 2 years and 4 months to clear the loan ?????

(Hint: Find A for 2 year with interest is Compounded yearly and then Find S.I. on the 2nd year Amount for 4/12 years.)

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Answers

Answered by mathdude500
43

\large\underline{\sf{Solution-}}

Amount borrowed, i.e. Principal, P = Rs 26, 400

Rate of interest, r = 15 % per annum compounded annually

Time, n = 2 years and 4 months = 2 1/3 years

We know,

Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n q/s year is given by

\boxed{\tt{ Amount = P {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \bigg[1 + \dfrac{r}{100} \times \dfrac{q}{s}  \bigg] \: }} \\

So, on substituting the values, we get

\rm \:  Amount = 26400 {\bigg[1 + \dfrac{15}{100} \bigg]}^{2} \bigg[1 + \dfrac{15}{100} \times \dfrac{1}{3}  \bigg] \: \\

\rm \:  Amount = 26400 {\bigg[1 + \dfrac{3}{20} \bigg]}^{2} \bigg[1 + \dfrac{1}{20}  \bigg] \: \\

\rm \:  Amount = 26400 {\bigg[ \dfrac{20 + 3}{20} \bigg]}^{2} \bigg[\dfrac{20 + 1}{20}  \bigg] \: \\

\rm \:  Amount = 26400 {\bigg[ \dfrac{23}{20} \bigg]}^{2} \bigg[\dfrac{21}{20}  \bigg] \: \\

\rm\implies \:Amount = 36659.70

So, amount that she have to pay at the end of 2 years and 4 months to clear the loan is Rs 36659. 70

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ADDITIONAL INFORMATION

1. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years is given by

\boxed{\tt{ Amount = P {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: }} \\

2. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded semi - annually for n years is given by

\boxed{\tt{ Amount = P {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \: }} \\

3. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded quarterly for n years is given by

\boxed{\tt{ Amount = P {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: }} \\

4. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded monthly for n years is given by

\boxed{\tt{ Amount = P {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} \: }} \\

Answered by Dalfon
311

Step-by-step explanation:

Given that Kamala borrowed Rs.26,400 from a Bank to Bye a Scooter bat a rate of 15% p.a. Compounded Yearly and she pay at the end of 2 years and 4 months to clear the loan.

We need to find out the amount payed by her at the end of 2 years and 4 months to clear the loan.

Now,

Amount for 2 years = P (1 + R/100)^T

Substitute the known values,

= 26400 (1 + 15/100)²

= 26400 (115/100)²

= 264 (115 × 115)/100

= 34914

Hence, the amount is Rs. 34914.

Also,

Interest for 4 months or 1/3 year = (P × R × T)/100

= (34914 × 15 × (1/3)/100

= (34914 × 5)/100

= 34914/20

= 1745.70

Total amount = 34914 + 1745.70 = Rs. 36659.7

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