Question:
William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9000
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 = $9000 – $5000 = $4000
Thus, Simple Interest = $4000
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 × 4000/5000 × 8
= 400000/40000
= 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) = $5000
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4000 (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 $5000
= 8/100 × 5000
= 8 × 5000/100
= 40000/100 = 400
Thus, simple Interest for 1 year = $400
Now,
∵ If the simple Interest is $400, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/400 years
∴ If the simple Interest is $4000, then the time = 1/400 × 4000 years
= 1 × 4000/400 years
= 4000/400 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(2) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(4) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(9) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.