Question:
Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10320
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 = $10320 – $6000 = $4320
Thus, Simple Interest = $4320
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 × 4320/6000 × 9
= 432000/54000
= 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) = $6000
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4320 (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 $4320, then the time = 1/540 × 4320 years
= 1 × 4320/540 years
= 4320/540 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?
(2) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.
(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?
(7) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?
(10) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.