Question:
Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9774
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 = $9774 – $5400 = $4374
Thus, Simple Interest = $4374
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 × 4374/5400 × 9
= 437400/48600
= 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) = $5400
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4374 (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 $5400
= 9/100 × 5400
= 9 × 5400/100
= 48600/100 = 486
Thus, simple Interest for 1 year = $486
Now,
∵ If the simple Interest is $486, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/486 years
∴ If the simple Interest is $4374, then the time = 1/486 × 4374 years
= 1 × 4374/486 years
= 4374/486 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.
(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(4) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
(5) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 6% simple interest?
(10) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.