Simple and Compound Interest

UPSC CSAT Maths

Introduction

  • Concept of time value of money: The value of money is not constant. This is one of the principal facts on which the entire economic world is based. A rupee today will not be equal to a rupee tomorrow. Hence, a rupee borrowed today cannot be repaid by a rupee tomorrow. This is the basic need for the concept of interest. The rate of interest is used to determine the difference between what is borrowed and what is repaid.

There are two bases on which interests are calculated:

  • Simple Interest: It is calculated on the basis of a basic amount borrowed for the entire period at a particular rate of interest. The amount borrowed is the principal for the entire period of borrowing.

  • Compound Interest: The interest of the previous year/s is/are added to the principal for the calculation of the com- pound interest.

  • Important Terminologies

  • The man who lends money is the Creditor and the man who borrows money is the Debtor.

  • The amount of money that is initially borrowed is called the Capital or Principal money.

  • The period for which money is deposited or borrowed is called Time.

  • The extra money that will be paid or received for the use of the principal after a certain period is called the Total Interest on the capital.

  • The sum of the principal and the interest at the end of any time is called the Amount.

So, Amount = Principal + Total Interest

  • Rate of Interest is the rate at which the interest is calculated and is always specified in percentage terms.

Simple Interest
I = p×t×r
Where,
P - Principal; t- time, r- rate of interest (per cent per annum)
Total Amount = I + P

Compound Interest
Let principal = P, time = t years and rate = r% per annum and let A be the total amount at the end of n years, then
A = (1+r/100)^t


Practice Questions

1. Rs. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.
a. 1380
b. 1290
c. 1470
d. 1200

2. Rs. 2100 is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.
a. Rs. 2300
b. Rs. 2315.25
c. Rs. 2425.5
d. Rs. 2447.5

3. Find the difference between the simple and the compound interest at 5% per annum for 2 years on a principal of Rs. 2000.
a. 5
b. 105
c. 4.5
d. None of these

4. In what time will Rs 500 give Rs 50 as interest at the rate of 5% per annum simple interest?
a. 2 years
b. 3 years
c. 4 years
d. 5 years

5. If the difference between the simple interest and compound interest on some principal amount at 20% per annum for 3 years is Rs 48, then the principal amount must be
a. 550
b. 500
c. 375
d. 400

6. A sum of money doubles itself in 5 years. In how many years will it become four-fold (if interest is compounded)?
a. 15
b. 10
c. 20
d. 12

7. A person bought a refrigerator worth Rs. 22,800 with 12.5% interest compounded yearly. At the end of first year he paid Rs. 8,650 and at the end of second year Rs. 9,125. How much will he have to pay at the end of third year to clear the debt? (UPSC 2017)
a. 9,990
b. 10,000
c. 10,590
d. 11,250

8. The simple interest on a sum of money is 25% of the principal, and the rate per annum is equal to the number of years. Find the rate percent.
a. 4.5%
b. 6%
c. 5%
d. 8%

9. If the difference between compound and simple interest on a certain sum of money for 3 years at 10% per annum is ₹310, what is the sum?
a. ₹8000
b. ₹1000
c. ₹10000
d. ₹5000

10. After how many years will a sum of ₹12,500 become ₹17,500at a rate of 10% per annum?
a. 2 years
b. 3 years
c. 4 years
d. 5 years


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