Tuesday, April 8, 2014

Mathematics Model Questions for PA/SA Exams on Interest

Mathematics Model Questions for PA/SA Exams on Interest

Before solving the problem Know Interest Formula

When a sum of money is borrowed for a period, an extra amount has to be paid along with the borrowed money. The fixed rate of the extra amount is called interest. The interest are of two types: simple interest and compound interest.

Simple interest is the interest paid at the end of the period. Compound interest is the total interest that includes the original interest and the interest of the new principal which is obtained by adding the original principal to the due interest.

The Interest formula is given as,

Solved  examples
Question 1.  A sum of Rs5000 is borrowed and the rate is 8%. What is the simple and compound interest for 2 years?
Solution,
Simple interest= principal *rate*time
Simple interest=5000 * 8/100 * 2
Simple interest=800
The Simple interest for 2 years is Rs800
Compound interest = principal( 1+rate ) time –principal
Compound interest= 5000 (1+8/100)2 – 5000
Compound interest=5000*1.1664-5000
Compound interest=832
The Compound interest for 2 years is Rs 832

Question no 2. A sum of Rs 200000 is borrowed and the rate is 10%. What is the simple and compound interest for 5 years?

Solution,
Simple interest= principal *rate*time
Simple interest=20000 * 10/100 * 5
Simple interest=10000
The Simple interest for 5 years is Rs10000
Compound interest = principal( 1+rate ) time –principal
Compound interest= 20000 (1+10/100)5 – 20000
Compound interest=20000*1.61051-20000
Compound interest=12210.20
The Compound interest for 5 years is Rs 12210.20

Problems

1.   A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.35 lakhs has been instructed to beinvested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?

(A)Rs. 17.5 lakhs        (B)Rs. 21 lakhs         (C)Rs. 15 lakhs     (D)Rs. 20 lakhs     Ans : B

2. What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?

(A)2400          (B)2592          (C)2678            (D)2540      Ans : B

3. If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to treble if invested at the same rate of interest in a scheme where interest is computed using simple interest method?

(A)9 years     (B)22 years    (C)18 years      (D)33 years      Ans : B

4. The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually?

(A)6000         (B)6400         (C)7200         (D)9600         Ans : B

5. A man invests Rs.5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year.

(A)5624.32        (B)5630.50           (C)5788.125             (D)5627.20   Ans : A

6. The difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years?

(A)9000         (B)6250         (C)8530.80    (D)8780.80   Ans : D

7. Vijay invested Rs.50,000 partly at 10% and partly at 15%. His total income after a year was Rs.7000. How much did he invest at the rate of 10%?

(A)Rs.40,000      (B)Rs.40,000       C)Rs.12,000         (D)Rs.20,000           Ans : B

8. A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?

(A)25 years  (B)40 years  (C)33.4 years  (D)Cannot be determined  Ans : A

9. How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000,
if  it  is  invested at 12.5% p.a simple interest?

(A)8 years    (B)64 years  (C)72 years  (D)56 years  Ans : D

10. Rs. 5887 is divided between Shyam and Ram, such that Shyam’s share at the end of 9 years is equal to Ram’s share at the end of 11 years, compounded annually at the rate of 5%. Find the share of Shyam.

(A)2088         (B)2000         (C)3087         (D)None of these   Ans : C

Questions shared by helping mind  Shreya Sinha, Delhi

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