Question:
Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $9690
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are given
Formual 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 = $9690 – $5700 = $3990
Thus, Simple Interest = $3990
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 × 3990/5700 × 10
= 399000/57000
= 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) = $5700
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3990 (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 = 10% of Principal
= 10% of $5700
= 10/100 × 5700
= 10 × 5700/100
= 57000/100 = 570
Thus, simple Interest for 1 year = $570
Now,
∵ If the simple Interest is $570, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/570 years
∴ If the simple Interest is $3990, then the time = 1/570 × 3990 years
= 1 × 3990/570 years
= 3990/570 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(2) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(3) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?
(5) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(9) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.
(10) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.