Question:
Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11400
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 = $11400 – $6000 = $5400
Thus, Simple Interest = $5400
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 × 5400/6000 × 10
= 540000/60000
= 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) = $6000
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5400 (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 = 10% of Principal
= 10% of $6000
= 10/100 × 6000
= 10 × 6000/100
= 60000/100 = 600
Thus, simple Interest for 1 year = $600
Now,
∵ If the simple Interest is $600, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/600 years
∴ If the simple Interest is $5400, then the time = 1/600 × 5400 years
= 1 × 5400/600 years
= 5400/600 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(3) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
(4) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 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 2% simple interest for 7 years.
(6) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(9) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.