Question:
Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10148
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 = $10148 – $5900 = $4248
Thus, Simple Interest = $4248
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 × 4248/5900 × 9
= 424800/53100
= 8 years (using formula)
Thus, Time (T) = 8 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 = $4248 (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 $4248, then the time = 1/531 × 4248 years
= 1 × 4248/531 years
= 4248/531 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(2) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(3) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(5) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.
(8) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(10) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?