Question:
Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7548
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 = $7548 – $5100 = $2448
Thus, Simple Interest = $2448
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 × 2448/5100 × 6
= 244800/30600
= 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) = $5100
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2448 (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 $5100
= 6/100 × 5100
= 6 × 5100/100
= 30600/100 = 306
Thus, simple Interest for 1 year = $306
Now,
∵ If the simple Interest is $306, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/306 years
∴ If the simple Interest is $2448, then the time = 1/306 × 2448 years
= 1 × 2448/306 years
= 2448/306 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?
(2) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.
(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?
(4) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
(7) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(8) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(9) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(10) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.