Question:
Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11880
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $11880 – $6600 = $5280
Thus, Simple Interest = $5280
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 5280/6600 × 10
= 528000/66000
= 8 years (using formula)
Thus, Time (T) = 8 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $6600
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5280 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 10% of Principal
= 10% of $6600
= 10/100 × 6600
= 10 × 6600/100
= 66000/100 = 660
Thus, simple Interest for 1 year = $660
Now,
∵ If the simple Interest is $660, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/660 years
∴ If the simple Interest is $5280, then the time = 1/660 × 5280 years
= 1 × 5280/660 years
= 5280/660 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
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