Question:
Christopher took a loan of $6000 at the rate of 9% 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
10
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 9% 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 × 9
= 540000/54000
= 10 years (using formula)
Thus, Time (T) = 10 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 = $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 = 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 $5400, then the time = 1/540 × 5400 years
= 1 × 5400/540 years
= 5400/540 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?
(2) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?
(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(4) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(6) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?
(7) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?
(8) Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?