Question:
James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $5440
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 = $5440 – $4000 = $1440
Thus, Simple Interest = $1440
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 × 1440/4000 × 6
= 144000/24000
= 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) = $4000
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1440 (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 $4000
= 6/100 × 4000
= 6 × 4000/100
= 24000/100 = 240
Thus, simple Interest for 1 year = $240
Now,
∵ If the simple Interest is $240, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/240 years
∴ If the simple Interest is $1440, then the time = 1/240 × 1440 years
= 1 × 1440/240 years
= 1440/240 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(4) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(5) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(6) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(8) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?
(10) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.