Question:
William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8150
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 = $8150 – $5000 = $3150
Thus, Simple Interest = $3150
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 × 3150/5000 × 9
= 315000/45000
= 7 years (using formula)
Thus, Time (T) = 7 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 = $3150 (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 $3150, then the time = 1/450 × 3150 years
= 1 × 3150/450 years
= 3150/450 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?
(3) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?
(4) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(6) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(8) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.