Question:
Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $12600
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 = $12600 – $7000 = $5600
Thus, Simple Interest = $5600
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 × 5600/7000 × 10
= 560000/70000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $7000
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5600 (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 $7000
= 10/100 × 7000
= 10 × 7000/100
= 70000/100 = 700
Thus, simple Interest for 1 year = $700
Now,
∵ If the simple Interest is $700, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/700 years
∴ If the simple Interest is $5600, then the time = 1/700 × 5600 years
= 1 × 5600/700 years
= 5600/700 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.
(4) 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.
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.
(6) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.
(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(9) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(10) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.