Question:
Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10830
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 = $10830 – $5700 = $5130
Thus, Simple Interest = $5130
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 × 5130/5700 × 9
= 513000/51300
= 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) = $5700
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5130 (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 $5700
= 9/100 × 5700
= 9 × 5700/100
= 51300/100 = 513
Thus, simple Interest for 1 year = $513
Now,
∵ If the simple Interest is $513, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/513 years
∴ If the simple Interest is $5130, then the time = 1/513 × 5130 years
= 1 × 5130/513 years
= 5130/513 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(3) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(6) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?
(8) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?
(9) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.