Question:
William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9050
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 = $9050 – $5000 = $4050
Thus, Simple Interest = $4050
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 × 4050/5000 × 9
= 405000/45000
= 9 years (using formula)
Thus, Time (T) = 9 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) = 9% per annum
Simple Interest = $4050 (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 $5000
= 9/100 × 5000
= 9 × 5000/100
= 45000/100 = 450
Thus, simple Interest for 1 year = $450
Now,
∵ If the simple Interest is $450, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/450 years
∴ If the simple Interest is $4050, then the time = 1/450 × 4050 years
= 1 × 4050/450 years
= 4050/450 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?
(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(7) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(9) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.