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) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(5) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?
(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?