Q.1.The difference in simple interest and compound interest on a certain sum of money in 2 years at 10 % p.a. is Rs. 50. The sum is
a) Rs. 10000
b) Rs. 6000
c) Rs. 5000
d) Rs. 2000
e) None of these
Q.2. The difference in simple interest and compound interest on a certain sum of money in 2 years at 18 % p.a. is Rs. 162. The sum is
a) Rs. 4000
b) Rs. 5200
c) Rs. 4250
d) Rs. 5000
e) None of these
Q.3. The compound interest on a certain sum of money for 2 years is Rs. 208 and the simple interest for the same time at the same rate is Rs. 200. Find the rate %.
a) 5 %
b) 6 %
c) 7 %
d) 4 %
e) 8 %
Q.4.The difference between compound interest and simple interest on a certain sum for 2 years at 10 % is Rs. 25. The sum is
a) Rs. 1200
b) Rs. 2500
c) Rs. 750
d) Rs. 1250
e) Rs. 2000
Q.5.The simple interest on a certain sum for 3 years in Rs. 225 and the compound interest on the same sum for 2 years is Rs. 165. Find the rate percent per annum.
a) 20 %
b) 2.5 %
c) 5 %
d) 15 %
e) 7.5%
Q.6.The simple interest on a sum of money for 2 years is Rs. 150 and the compound interest on the same sum at same rate for 2 years is Rs. 155. The rate % p.a. is
a) 16 %
b) 20/3 %
c) 12 %
d) 10 %
e) None of these
Q7.Mihir’s capital is 5/4 times more than Tulsi’s capital. Tulsi invested her capital at 50 % per annum for 3 years (compounded annually). At what rate % p.a. simple interest should Mihir invest his capital so that after 3 years, they both have the same amount of capital?
a) 20/3 %
b) 10 %
c) 50/3 %
d) 1.728 %
e) None of these
Q8.The difference in simple interest and compound interest on a certain sum of money in 3 years at 10 % p.a. is Rs. 372. The sum is
a) Rs. 8000
b) Rs.9000
c) Rs. 10000
d) Rs. 12000
e) None of these
Q9.Sahil’s capital is 1/6 times more than Chaya’s capital. Chaya invested her capital at 20 % per annum for 2 years (compounded annually). At what rate % p.a. simple interest should Sahil invest his capital so that after 2 years, they both have the same amount of capital?
a) 10%
b) 11 5/7%
c) 20%
d) 13 5/7%
e) None of these
Q10.The difference in simple interest and compound interest on a certain sum of money in 3 years at 20 % p.a. is Rs. 640. The sum is
a) Rs. 5000
b) Rs. 8500
c) Rs. 8250
d) Rs. 6000
e) None of these
The difference between the compound interest and simple interest on a certain sum of money at 10% per annum for 2 years is Rs.500. Find the sum when the interest is compounded annually.
Answer
Verified
Hint: Let the sum be \[x\] rupees. We know the compound interest \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}\] , we need to find P. we know simple interest formula \[S.I = P \times \dfrac{r}{{100}} \times T\] . We know compound interest is the difference between amount and principal amount. Since the difference between compound and simple interest is given we can find the value of \[x\] .
Complete step-by-step answer:
We know,
\[A = P{\left( {1 +
\dfrac{r}{{100}}} \right)^n}\] , where A is amount, R is rate of interest, n is number of times the interest is compounded per year.
\[P = x\] , \[n = 2\] \[r = 10\] , substituting we get,
\[ \Rightarrow A = x{\left( {1 + \dfrac{{10}}{{100}}} \right)^2}\]
\[ \Rightarrow A = x{\left( {1 + \dfrac{1}{{10}}} \right)^2}\]
Taking L.C.M and simplifying we get,
\[ \Rightarrow A = x{\left( {\dfrac{{10 + 1}}{{10}}} \right)^2}\]
\[ \Rightarrow A =
x{\left( {\dfrac{{11}}{{10}}} \right)^2}\]
We know that compound interest is the difference between the amount of money accumulated after n years and the principal amount.
\[C.I = A - P\]
\[ \Rightarrow C.I = x{\left( {\dfrac{{11}}{{10}}} \right)^2} - x\] .
Now to find the simple interest we have, \[S.I = P \times \dfrac{r}{{100}} \times T\]
Substituting the known values,
\[ \Rightarrow S.I = x \times \dfrac{{10}}{{100}} \times 2\]
\[ \Rightarrow
S.I = x \times \dfrac{1}{{10}} \times 2\]
\[ \Rightarrow S.I = \dfrac{x}{5}\]
Given the difference between compound and simple interest is 500
\[ \Rightarrow C.I - S,I = 500\]
Substituting C.I and S.I we get
\[ \Rightarrow x{\left( {\dfrac{{11}}{{10}}} \right)^2} - x - \dfrac{x}{5} = 500\]
Simple division \[\dfrac{{11}}{{10}} = 1.1\] and \[\dfrac{1}{5} = 0.2\] we get,
\[ \Rightarrow x{(1.1)^2} - x - 0.2x = 500\]
\[ \Rightarrow 1.21x - 1x
- 0.20x = 500\]
\[ \Rightarrow 0.21x - 0.20x = 500\]
Taking x as common,
\[ \Rightarrow (0.21 - 0.20)x = 500\]
\[ \Rightarrow 0.01x = 500\]
\[ \Rightarrow x = \dfrac{{500}}{{0.01}}\]
Multiply numerator and denominator by 100.
\[ \Rightarrow x = 50,000\]
That is \[P = 50,000\] .
\[50,000\] Rupees is the sum when the interest is compounded annually.
So, the correct answer is “\[P = 50,000\]”.
Note: Here we used three formulas. Remember the formula for simple interest, compound interest and amount formula. We can also take P as P as it is, and solve for P. Above all we did is substituting the given data in the formula and simplifying. Principal amount is the initial amount you borrow or deposit.