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) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(2) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(3) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(8) 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.
(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.