Question:
Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9548
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 = $9548 – $6200 = $3348
Thus, Simple Interest = $3348
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 × 3348/6200 × 9
= 334800/55800
= 6 years (using formula)
Thus, Time (T) = 6 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) = $6200
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3348 (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 = 9% of Principal
= 9% of $6200
= 9/100 × 6200
= 9 × 6200/100
= 55800/100 = 558
Thus, simple Interest for 1 year = $558
Now,
∵ If the simple Interest is $558, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/558 years
∴ If the simple Interest is $3348, then the time = 1/558 × 3348 years
= 1 × 3348/558 years
= 3348/558 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(2) 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.
(3) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.
(5) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 3 years.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.
(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.