# S.I. & C.I. (20)

1. A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times?
1. 10 years
2. 8 years
3. 6 years
4. 12 years

Explanation :-

Let P = Rs.100   Rate = R%   A = Rs. 200   Time = 4 years.
Then ,   A = P*[1+ (r/100)]n
200 = 100*[1+(R/100)]4
2 = [1+(R/100)]4   ————- (1)
If sum become 8 times in the time T  years,
Then,8 = (1+(R/100))T
23 = (1+(R/100))T ————- (2)
By putting value of 2 from equation (1) in equation (2)
([1+(R/100)]4)3 = (1+(R/100))T
[1+(R/100)]12 = (1+(R/100))T
Thus, T = 12 years.

2. On what sum will the compound interest for 2 1⁄2 years at 10% amount to Rs. 31762.5?
1. Rs.5000
2. Rs.20000
3. Rs.25000
4. Rs.30000

Explanation :-

= [ P(1+10/100)^2 ] [ (1+10/200)^T ] =  Rs. 31762.5
P [(11/10)^2] × (21/2031762.5
= (31762.5×20×10×10) / (21×11×11) = (1512.5×20×10×10)/(11×11)
P = (137.5×20×10×10)/11 =12.5×20×10×10 Rs. 25000

3. The compound interest on Rs. 20,000 at 8% per annum is Rs. 3,328. What is the period (in year)?
1. 1 year
2. 4 years
3. 3 years
4. 2 years

Explanation :-

Let the period be t years.
Amount after t years = Rs.20000 + Rs.3328 = Rs. 23328
P(1+R/100)^23328
20000(1+8100)^T 23328/20000
(108/100)^T 23328/20000
(11664/10000) (108/100)^2
(108/100)^T = (108/100)^2
Therefore,   T = 2 years

4. A man borrows Rs. 20,000 at 10% compound interest. At the end of every year he pays Rs. 2000 as part repayment. How much does he still owe after three such installments?
1. Rs.24000
2. Rs.15000
3. Rs.20000
4. Rs.10000

Explanation :-

Principal (For 1st year)= Rs. 12500
Therefore Interest (for 1st year) = 20% of 12500 = Rs. 2500
Amount paid At the end of 1st year = Rs. 2000
Therefore , Principal (for 2nd year) = 12500 +2500 – 2000 = 13000
Therefore Interest (for 2nd year) = 20% of 13000 = Rs. 2600
Amount paid At the end of 2nd year = Rs. 2000
Therefore , Principal (for 3rd year) = 13000 +2600 – 2000 = 13600
Therefore Interest (for 3rd year) = 20% of 13600 = Rs. 2720
Amount paid At the end of 3rd year = Rs. 2000
Therefore , Amount after three installments = 13600 +2720 – 2000 = Rs.14320

5. The present worth of Rs. 242 due in 2 years at 10% per annum compound interest is:
1. Rs. 180
2. Rs. 240
3. Rs. 220
4. Rs. 200