Question:
Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4600
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8740
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 = $8740 – $4600 = $4140
Thus, Simple Interest = $4140
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 × 4140/4600 × 9
= 414000/41400
= 10 years (using formula)
Thus, Time (T) = 10 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) = 9% per annum
Simple Interest = $4140 (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 $4600
= 9/100 × 4600
= 9 × 4600/100
= 41400/100 = 414
Thus, simple Interest for 1 year = $414
Now,
∵ If the simple Interest is $414, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/414 years
∴ If the simple Interest is $4140, then the time = 1/414 × 4140 years
= 1 × 4140/414 years
= 4140/414 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.
(3) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?
(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.
(9) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?
(10) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.