Question:
Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6300
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10332
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 = $10332 – $6300 = $4032
Thus, Simple Interest = $4032
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 × 4032/6300 × 8
= 403200/50400
= 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) = $6300
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4032 (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 = 8% of Principal
= 8% of $6300
= 8/100 × 6300
= 8 × 6300/100
= 50400/100 = 504
Thus, simple Interest for 1 year = $504
Now,
∵ If the simple Interest is $504, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/504 years
∴ If the simple Interest is $4032, then the time = 1/504 × 4032 years
= 1 × 4032/504 years
= 4032/504 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
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(3) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
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