Question:
Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7242
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 = $7242 – $5100 = $2142
Thus, Simple Interest = $2142
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 × 2142/5100 × 6
= 214200/30600
= 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) = $5100
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2142 (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 $2142, then the time = 1/306 × 2142 years
= 1 × 2142/306 years
= 2142/306 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.
(2) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(3) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.
(5) 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.
(6) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(8) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.