An automobile financier claims to be lending money at simple interest, but he in

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Question
An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:
Options
A. 10%
B. 10.25%
C. 10.5%
D. None of these

Correct Answer

10.25%

Explanation
Let the sum be Rs. 100. Then,

S.I. for first 6 months = Rs.	❨	100 x 10 x 1	❩	= Rs. 5
		100 x 2

S.I. for last 6 months = Rs.	❨	105 x 10 x 1	❩	= Rs. 5.25
		100 x 2

So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25

∴ Effective rate = (110.25 - 100) = 10.25%

Simple Interest problems

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1. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
Options
A. 5%
B. 7%
C. 7 ¹⁄₈%
D. 10%

2. Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
Options
A. Rs. 6400
B. Rs. 6500
C. Rs. 7200
D. Rs. 7500
E. None of these

3. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:
Options
A. 5%
B. 8%
C. 12%
D. 15%

4. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
Options
A. Rs. 650
B. Rs. 690
C. Rs. 698
D. Rs. 700

5. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
Options
A. Rs. 4462.50
B. Rs. 8032.50
C. Rs. 8900
D. Rs. 8925
E. None of these

6. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
Options
A. Rs. 2000
B. Rs. 10,000
C. Rs. 15,000
D. Rs. 20,000

7. A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?
Options
A. 3.6%
B. 4.5%
C. 5%
D. 6%
E. None of these

8. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
Options
A. Rs. 35
B. Rs. 245
C. Rs. 350
D. Cannot be determined
E. None of these

9. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6¼% p.a for 2 years. Find his gain in the transaction per year.
Options
A. Rs. 112.50
B. Rs. 125
C. Rs. 225
D. Rs. 167.50

10. What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?
Options
A. 1 : 3
B. 1 : 4
C. 2 : 3
D. Data inadequate
E. None of these

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