Question:
Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 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) = 10% per annum
Amount (A) = $7360
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 = $7360 – $4600 = $2760
Thus, Simple Interest = $2760
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 × 2760/4600 × 10
= 276000/46000
= 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) = 10% per annum
Simple Interest = $2760 (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 = 10% of Principal
= 10% of $4600
= 10/100 × 4600
= 10 × 4600/100
= 46000/100 = 460
Thus, simple Interest for 1 year = $460
Now,
∵ If the simple Interest is $460, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/460 years
∴ If the simple Interest is $2760, then the time = 1/460 × 2760 years
= 1 × 2760/460 years
= 2760/460 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(3) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(4) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.
(8) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(10) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.