Question:
Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9360
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 = $9360 – $6000 = $3360
Thus, Simple Interest = $3360
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 × 3360/6000 × 8
= 336000/48000
= 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) = $6000
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3360 (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 = 8% of Principal
= 8% of $6000
= 8/100 × 6000
= 8 × 6000/100
= 48000/100 = 480
Thus, simple Interest for 1 year = $480
Now,
∵ If the simple Interest is $480, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/480 years
∴ If the simple Interest is $3360, then the time = 1/480 × 3360 years
= 1 × 3360/480 years
= 3360/480 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?
(4) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(6) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(8) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?