Question:
Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $10780
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 = $10780 – $7000 = $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 × 3780/7000 × 6
= 378000/42000
= 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) = $7000
Rate of Simple Interest (R) = 6% 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 = 6% of Principal
= 6% of $7000
= 6/100 × 7000
= 6 × 7000/100
= 42000/100 = 420
Thus, simple Interest for 1 year = $420
Now,
∵ If the simple Interest is $420, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/420 years
∴ If the simple Interest is $3780, then the time = 1/420 × 3780 years
= 1 × 3780/420 years
= 3780/420 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?
(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(3) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(6) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(9) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.