Question:
Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7668
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 = $7668 – $5400 = $2268
Thus, Simple Interest = $2268
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 × 2268/5400 × 6
= 226800/32400
= 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) = $5400
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2268 (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 $5400
= 6/100 × 5400
= 6 × 5400/100
= 32400/100 = 324
Thus, simple Interest for 1 year = $324
Now,
∵ If the simple Interest is $324, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/324 years
∴ If the simple Interest is $2268, then the time = 1/324 × 2268 years
= 1 × 2268/324 years
= 2268/324 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.
(4) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?
(5) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(9) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(10) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?