Question:
Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $6256
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 = $6256 – $4600 = $1656
Thus, Simple Interest = $1656
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 × 1656/4600 × 6
= 165600/27600
= 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) = $4600
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $1656 (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 = 6% of Principal
= 6% of $4600
= 6/100 × 4600
= 6 × 4600/100
= 27600/100 = 276
Thus, simple Interest for 1 year = $276
Now,
∵ If the simple Interest is $276, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/276 years
∴ If the simple Interest is $1656, then the time = 1/276 × 1656 years
= 1 × 1656/276 years
= 1656/276 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(4) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(6) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(7) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?
(10) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.