Question:
John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7040
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 = $7040 – $4400 = $2640
Thus, Simple Interest = $2640
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 × 2640/4400 × 10
= 264000/44000
= 6 years (using formula)
Thus, Time (T) = 6 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) = $4400
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $2640 (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 $4400
= 10/100 × 4400
= 10 × 4400/100
= 44000/100 = 440
Thus, simple Interest for 1 year = $440
Now,
∵ If the simple Interest is $440, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/440 years
∴ If the simple Interest is $2640, then the time = 1/440 × 2640 years
= 1 × 2640/440 years
= 2640/440 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(5) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(7) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(8) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?