Question:
John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6248
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 = $6248 – $4400 = $1848
Thus, Simple Interest = $1848
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 × 1848/4400 × 6
= 184800/26400
= 7 years (using formula)
Thus, Time (T) = 7 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 = $1848 (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 $1848, then the time = 1/264 × 1848 years
= 1 × 1848/264 years
= 1848/264 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?
(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(6) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(7) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.