Question:
John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 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) = 6% per annum
Amount (A) = $5984
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 = $5984 – $4400 = $1584
Thus, Simple Interest = $1584
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 × 1584/4400 × 6
= 158400/26400
= 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) = 6% per annum
Simple Interest = $1584 (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 $4400
= 6/100 × 4400
= 6 × 4400/100
= 26400/100 = 264
Thus, simple Interest for 1 year = $264
Now,
∵ If the simple Interest is $264, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/264 years
∴ If the simple Interest is $1584, then the time = 1/264 × 1584 years
= 1 × 1584/264 years
= 1584/264 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.
(2) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?
(4) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(8) 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.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.