# compound interest

11.

Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
A.     Rs. 1550    B.     Rs. 1650
C.     Rs. 1750    D.     Rs. 2000

Explanation:

C.I.
= Rs.         4000 x         1 +     10         2     – 4000
100

= Rs.         4000 x     11     x     11     – 4000
10     10
= Rs. 840.

Sum = Rs.         420 x 100         = Rs. 1750.
3 x 8

12.

If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
A.     Rs. 51.25    B.     Rs. 52
C.     Rs. 54.25    D.     Rs. 60

Explanation:

Sum = Rs.         50 x 100         = Rs. 500.
2 x 5

Amount
= Rs.         500 x         1 +     5         2
100

= Rs.         500 x     21     x     21
20     20
= Rs. 551.25

C.I. = Rs. (551.25 – 500) = Rs. 51.25

13.

The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
A.     Rs. 2.50    B.     Rs. 3
C.     Rs. 3.75    D.     Rs. 4
E.     None of these

Explanation:

S.I. = Rs         1200 x 10 x 1         = Rs. 120.
100

C.I. = Rs.         1200 x         1 +     5         2     – 1200         = Rs. 123.
100

Difference = Rs. (123 – 120) = Rs. 3.

14.

The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
A.     8    B.     10
C.     12    D.     Cannot be determined
E.     None of these

Explanation:

15000 x         1 +     R         2     – 15000         –         15000 x R x 2         = 96
100     100

15000             1 +     R         2     – 1 –     2R         = 96
100     100

15000         (100 + R)2 – 10000 – (200 x R)         = 96
10000

R2 =         96 x 2         = 64
3

R = 8.

Rate = 8%.

15.

The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
A.     Rs. 400    B.     Rs. 500
C.     Rs. 600    D.     Rs. 800

Explanation:

Let the sum be Rs. P.

Then,         P         1 +     10         2     – P         = 525
100

P             11         2     – 1         = 525
10

P =         525 x 100         = 2500.
21

Sum = Rs . 2500.

So, S.I. = Rs.         2500 x 5 x 4         = Rs. 500
100