Question:
Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9240
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 = $9240 – $6000 = $3240
Thus, Simple Interest = $3240
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 × 3240/6000 × 6
= 324000/36000
= 9 years (using formula)
Thus, Time (T) = 9 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) = $6000
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3240 (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 $6000
= 6/100 × 6000
= 6 × 6000/100
= 36000/100 = 360
Thus, simple Interest for 1 year = $360
Now,
∵ If the simple Interest is $360, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/360 years
∴ If the simple Interest is $3240, then the time = 1/360 × 3240 years
= 1 × 3240/360 years
= 3240/360 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(3) 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.
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(5) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 4% simple interest?
(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(9) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
(10) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.