Question:
Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9780
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 = $9780 – $6000 = $3780
Thus, Simple Interest = $3780
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 × 3780/6000 × 9
= 378000/54000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $6000
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3780 (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 $6000
= 9/100 × 6000
= 9 × 6000/100
= 54000/100 = 540
Thus, simple Interest for 1 year = $540
Now,
∵ If the simple Interest is $540, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/540 years
∴ If the simple Interest is $3780, then the time = 1/540 × 3780 years
= 1 × 3780/540 years
= 3780/540 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(2) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(5) How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?
(6) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(7) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.