Question:
Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10679
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 = $10679 – $5900 = $4779
Thus, Simple Interest = $4779
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 × 4779/5900 × 9
= 477900/53100
= 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) = $5900
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4779 (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 $5900
= 9/100 × 5900
= 9 × 5900/100
= 53100/100 = 531
Thus, simple Interest for 1 year = $531
Now,
∵ If the simple Interest is $531, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/531 years
∴ If the simple Interest is $4779, then the time = 1/531 × 4779 years
= 1 × 4779/531 years
= 4779/531 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(2) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?
(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(5) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(6) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(9) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.