Let the time period be T years. Given, P = Rs 1500, C.I. = Rs 496.50, R = 20% p.a. compounded semi-annually.  Thus, the time period is 1 year 6 months.
Question 24 Compound Interest Exercise 2.2 Next
Answer:
(i) It is given that Principal (P) = ₹ 1500 CI = ₹ 496.50 So the amount (A) = P + SI Substituting the values = 1500 + 496.50 = ₹ 1996.50 Rate (r) = 10% p.a. We know that Here Time n = 3 years (ii) It is given that Principal (P) = ₹ 12500 CI = ₹ 3246.40 So the amount (A) = P + CI Substituting the values = 12500 + 3246.40 = ₹ 15746.40 Rate (r) = 8% p.a. We know that By further calculation Here Period = 3 years
Was This helpful? Answer Hint: Now first we will find the final amount. Final amount is given by Principal amount + Interest. Now once we have the final amount we will use the formula for compound interest.$A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}$ Now since the Interest in compounded half yearly we will take n=2. Hence we have $A=P{{\left( 1+\dfrac{r}{200} \right)}^{2t}}$. Now we know P which is principal amount, A which is final amount and r which is rate of interest. Hence we will substitute the values and find t. Complete step-by-step answer: Now we are given that Rs 1500 yields Rs 496.50.Hence we have Principal = 1500 and interest = 496.50Now final amount = Principal + interest = 1500 + 496.5.Hence final amount = 1996.5 Rs. Now we know that the final amount of compound interest compounded annually is given by $A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}$Here we have the final amount = 1996.5, principal amount = 1500.rate of interest = 20 percent = $\dfrac{20}{100}=0.2$ , and n = 2 since the compound interest will be compounded 2 times a year.Now substituting these values in the formula we have. $1996.5=1500{{\left( 1+\dfrac{0.2}{2} \right)}^{2t}}$Dividing the equation by 1500 we get$\dfrac{1996.5}{1500}={{\left( 1+0.1 \right)}^{2t}}$$\Rightarrow \dfrac{1331}{1000}={{\left( 1.1 \right)}^{2t}}$$\Rightarrow \dfrac{1331}{1000}={{\left( \dfrac{11}{10} \right)}^{2t}}$Hence we get $2t=3$. Now dividing this equation by 2 we get$t=\dfrac{3}{2}=1\dfrac{1}{2}$Hence we have one and half years. Hence we get the money that is supposed to be kept for one and a half year so that will be Rs 1500 yield Rs 496.50.Note: Note that in the formula of compound interest n stands for the number of times the interest will be compounded in a year. Hence if the interest is compounded half yearly, in one year the interest will be compounded 2 times. Hence n = 2 and not $\dfrac{1}{2}$ . Given: P=Rs. 1,500; C.I.= Rs. 496.50 and r = 20% Then, C.I. = `"P"[( 1 + r/[2 xx 100])^(n xx 2) - 1]` ⇒ 496.50 = 1,500`[( 1 + 20/[2 xx 100])^(n xx 2) - 1]` ⇒ `[496.50]/[1500] = (11/10)^(2n) - 1` ⇒ `331/1000 + 1 = (11/10)^(2n)` ⇒ `1331/1000 = (11/10)^(2n)` ⇒ `(11/10)^3 = (11/10)^(2n)` On comparing, we get, 2n = 3 ⇒ n = `1 1/2` years |
In what time will rupees 1500 yield rupees 496.50 as compound interest at 20% per year compounded half yearly?
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