Question:
Donald took a loan of $7000 at the rate of 8% 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
10
Solution And Explanation
Solution
Given,
Principal (P) = $7000
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $12600
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 × 8
= 560000/56000
= 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) = $7000
Rate of Simple Interest (R) = 8% 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 = 8% of Principal
= 8% of $7000
= 8/100 × 7000
= 8 × 7000/100
= 56000/100 = 560
Thus, simple Interest for 1 year = $560
Now,
∵ If the simple Interest is $560, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/560 years
∴ If the simple Interest is $5600, then the time = 1/560 × 5600 years
= 1 × 5600/560 years
= 5600/560 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(7) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.