Question:
Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10664
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 = $10664 – $6200 = $4464
Thus, Simple Interest = $4464
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 × 4464/6200 × 9
= 446400/55800
= 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) = $6200
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4464 (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 $4464, then the time = 1/558 × 4464 years
= 1 × 4464/558 years
= 4464/558 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(4) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(5) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(6) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(8) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.
(10) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.