Question:
Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8378
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 = $8378 – $5900 = $2478
Thus, Simple Interest = $2478
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 × 2478/5900 × 6
= 247800/35400
= 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) = $5900
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2478 (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 = 6% of Principal
= 6% of $5900
= 6/100 × 5900
= 6 × 5900/100
= 35400/100 = 354
Thus, simple Interest for 1 year = $354
Now,
∵ If the simple Interest is $354, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/354 years
∴ If the simple Interest is $2478, then the time = 1/354 × 2478 years
= 1 × 2478/354 years
= 2478/354 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(2) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.
(5) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
(6) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(7) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(9) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.