Question:
Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 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) = 7% per annum
Amount (A) = $8791
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 = $8791 – $5900 = $2891
Thus, Simple Interest = $2891
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 × 2891/5900 × 7
= 289100/41300
= 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) = 7% per annum
Simple Interest = $2891 (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 = 7% of Principal
= 7% of $5900
= 7/100 × 5900
= 7 × 5900/100
= 41300/100 = 413
Thus, simple Interest for 1 year = $413
Now,
∵ If the simple Interest is $413, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/413 years
∴ If the simple Interest is $2891, then the time = 1/413 × 2891 years
= 1 × 2891/413 years
= 2891/413 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.
(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.
(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(7) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(9) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
(10) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.