Question:
Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $13600
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 = $13600 – $6800 = $6800
Thus, Simple Interest = $6800
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 × 6800/6800 × 10
= 680000/68000
= 10 years (using formula)
Thus, Time (T) = 10 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) = $6800
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $6800 (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 = 10% of Principal
= 10% of $6800
= 10/100 × 6800
= 10 × 6800/100
= 68000/100 = 680
Thus, simple Interest for 1 year = $680
Now,
∵ If the simple Interest is $680, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/680 years
∴ If the simple Interest is $6800, then the time = 1/680 × 6800 years
= 1 × 6800/680 years
= 6800/680 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.
(2) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(5) If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(8) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(10) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.