Question:
James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7240
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 = $7240 – $4000 = $3240
Thus, Simple Interest = $3240
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 × 3240/4000 × 9
= 324000/36000
= 9 years (using formula)
Thus, Time (T) = 9 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) = $4000
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3240 (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 = 9% of Principal
= 9% of $4000
= 9/100 × 4000
= 9 × 4000/100
= 36000/100 = 360
Thus, simple Interest for 1 year = $360
Now,
∵ If the simple Interest is $360, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/360 years
∴ If the simple Interest is $3240, then the time = 1/360 × 3240 years
= 1 × 3240/360 years
= 3240/360 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(4) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?
(7) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
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