Question:
Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10758
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 = $10758 – $6600 = $4158
Thus, Simple Interest = $4158
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 × 4158/6600 × 7
= 415800/46200
= 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) = $6600
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4158 (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 = 7% of Principal
= 7% of $6600
= 7/100 × 6600
= 7 × 6600/100
= 46200/100 = 462
Thus, simple Interest for 1 year = $462
Now,
∵ If the simple Interest is $462, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/462 years
∴ If the simple Interest is $4158, then the time = 1/462 × 4158 years
= 1 × 4158/462 years
= 4158/462 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(2) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.
(4) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(7) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(8) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(10) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.