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Directions : Read the following questions carefully and choose the right answer.
1
A man lent Rs. 4500 at 30% compound interest per annum for 3 years. What is the difference between the interest earned by the man in the 2nd year only and the interest earned by the man in the 3rd year only?
» Explain it
C
Interest earned by the man on 2nd year

= 4500 ×  [ { 1 +  ( 30 ) } 2  – 1 ]  –  ( 4500 × 30 × 1 )
100   100

= 4500 ×  ( 69 )  – 1350 = 3105 – 1350 = Rs. 1755
100

Interest earned by the man on 3rd year

= 4500 ×  [ { 1 +  ( 30 ) } 3  – 1 ]  – 4500 ×  [ { 1 +  ( 30 ) } 2  – 1 ]
100   100  

= 4500 ×  ( 1197 )  – 4500 ×  69  = 5386.5 – 3105 = Rs.2281.5
1000 100

Therefore, required difference = 2281.5 – 1755 = Rs. 526.5

Hence, option C is correct.
2
A man saves Rs.20,000 at the beginning of each year and puts the money in a bank that pays 10% interest per year, interest being compounded annually. What would be the total savings of the man at the end of 6 years?
» Explain it
B
The first Rs. 20000 would become 20000(1.1)6 after 6 years, the second will become 20000(1.1)5.the third will become 20000 (1.1)4, the fourth will become 20000 (1.1)3 , the fifth will become 20000(1.1)2 and the sixth will become 20000 (1.1).
 
Total amount = 20000 [(1.1) + (1.1)2 + (1.1)3 + (1.1)4 + (1.1)5 + (1.1)6]

= (20000) (1.1) [ 1 + (1.1) + (1.1)2 + (1.1)3 + (1.1)4 + (1.1)5]

= 22000  (1.1)6 – 1  = 22000 (7.72) = Rs. 169840
1.1 – 1

Hence, option B is correct.
3
A bank lent Rs. X to a farmer at 50/3% p.a for 1 year73 days. How much Compound interest the farmer had to pay if the Simple interest for the first year is Rs. 3000?
 
The values of Compound Interest and Sum lent are given in the options; choose the option which correctly states the above question.
» Explain it
B
Rate = 16  2  % =  1
3 6

P × R × T  = Rs. 3000
100

P = Rs. 18000

Let us suppose Principal = 36

Interest for 1st year = 6 (which is the simple interest)

Interest for 2nd year = 6 + 1 = 7

Interest for 73 days =  7 × 73  = 1.4
365

Total interest = 6 + 1.4 = 7.4

36 corresponds to 18000

1 will correspond to 500

7.4 will correspond to 500 × 7.4 = Rs. 3700

So, the Compound Interest for 1 year 73 days is Rs. 3700 and the Sum lent to the farmer is Rs. 18000.

Hence, option B is correct.
4
Shyam deposited Rs. 80000 in a bank which pays 10% compound interest for 2 years. Then after 2 years, he started a business with amount (sum + interest) along with Ram, with capital of Rs. 60,000. Shyam invested for 6 months and left. Ram invested for the whole year. What will be the ratio of their profits at the end of the year?
» Explain it
B
Capital of Shyam = Rs. 80,000

Rate of Interest = 10%

Time for which he deposited in bank = 2 years

Amount = 80000  ( 1 +  10 ) 2
100  

 Amount =  80000 × 121  = Rs. 96800
100

Investment of Shyam in business = Rs. 96800

Investment of Ram in business = Rs. 60000

Ratio of their profits =   96800 × 6
60000 × 12

Ratio =  968 : 1200 = 121 : 150

Hence, option B is correct.
5
A man takes a loan of Rs 216000 from a bank, to be returned in three years at a rate of 16.67% p.a. compound interest. The man returns Rs 84000 and Rs 58000 after first and second year. How much money will he have to return after third year to settle the loan?
» Explain it
A
Money took = Rs 216000

Amount after first year

= 216000 ×  ( 1 +  16.67 )  = 216000 ×  7  = 252000
100 6

Amount paid after first year = 84000, amount remaining = 252000 – 84000 = 168000

Amount to be paid after second year

=  7  × 168000 = 196000
6

Amount paid after second year = 58000, amount remaining = 196000 – 58000 = 138000

Amount to paid after third year

=  7  × 138000 = Rs 161000
6

Hence, option A is correct.
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