Question:
Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10440
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 = $10440 – $5800 = $4640
Thus, Simple Interest = $4640
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 × 4640/5800 × 8
= 464000/46400
= 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) = $5800
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4640 (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 = 8% of Principal
= 8% of $5800
= 8/100 × 5800
= 8 × 5800/100
= 46400/100 = 464
Thus, simple Interest for 1 year = $464
Now,
∵ If the simple Interest is $464, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/464 years
∴ If the simple Interest is $4640, then the time = 1/464 × 4640 years
= 1 × 4640/464 years
= 4640/464 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(3) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(6) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(8) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(10) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.