Answer
Hint: To solve this type of problem, first calculate the final amount needed to pay after two year then subtract this final amount to the given principal amount to calculate the compound interest in two years.
Complete Step-by-step solution
Given principal amount is P =Rs 2000
Time to repay the amount is N = 2 years
Rate of interest is R =5 % per annum
To find the amount of compound interest after 2 years
C.I. = ?
To calculate the compound interest first
we will calculate the final amount that we need to pay after 2 year
We know that the formula to calculate the final amount
$$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^N}$$
On putting the given values
$$A = 2000 \times {\left( {1 + \dfrac{{5}}{{100}}} \right)^2}$$
On simplification
$$A = 20000 \times \dfrac{{441}}{{400}}$$
$$A = 2205$$
Now we will calculate the compound interest
We know that
∴ $$C.I. = A - P$$
On putting the values of A and P
We get
$$ =
Rs.2205 - Rs.2000$$
On subtracting
We get $$ = Rs.205$$
Hence the compound interest that needs to be paid after two year will be equal to Rs 205.
Note: The interest rate for the first year in compound interest is the same as that in case of simple interest, Other than the first year, the interest compounded annually is always greater than that in case of simple interest.
>When calculating compound interest, the number of compounding
periods makes a significant difference. The basic rule is that the higher the number of compounding periods, the greater the amount of compound interest.
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