"Question 3 Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?
Class 8 Comparing Quantities Page 134"
Answers
Simple Interest
If the principal remains the same throughout the loan period then the interest calculated on this principle is called the simple interest.
Principal (P): The original sum of money loaned/deposited. Also known as capital.
Time (T): The duration for which the money is borrowed/deposited.
Rate of Interest (R): The percent of interest that you pay for money borrowed, or earn for money deposited
Simple interest is calculated as
S.I= (P×R×T)/100
Total amount at the end of time period
A= P + SI
compound interest.
The time Period after which interest is added each time to form a new principal is called the conversion period and the interest so obtained is called a compound interest.
If the conversion period is 1 year then the interest is said to be compounded annually.
The main difference between the simple interest and compound interest on a certain sum is that in the case of simple interest the principal remains constant throughout wheras in the case of compound interest it goes on changing periodically.
The above formula is the interest compounded annually
A= P(1+r/100)^n
Compound interest= A-P
Where A is the amount ,
P the principal,
r the rate percent per conversion period and n is the number of conversion
periods
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Given:
Principal (P) = ₹12,500,
Time (T)= 3 years,
Rate of interest (R)
= 12% p.a.
Simple Interest for Fabina = (P×R×T)/100
= (12500× 12× 3)/100
= 125× 36
= ₹ 4,500
Amount for Radha,
Given:
P = ₹ 12,500, R = 10% n= 3 years
Amount (A) = P(1+R/100)^n
= 12500(1+10/100)³
= 12500( 1+1/10)³
= 12500× (11/10)³
= (12500 ×11×11×11)/1000
=125×1331/10= 166375/10
= Rs. 16,637.50
C.I. for Radha = A – P
= ₹16,637.50 – ₹12,500 = ₹ 4,137.50
Hence, Fabina pays more interest
= ₹4,500 – ₹4,137.50 = ₹ 362.50
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