Question:
Barbara took a loan of $5100 at the rate of 7% 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
6
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (R) = 7% 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 × 7
= 214200/35700
= 6 years (using formula)
Thus, Time (T) = 6 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) = 7% 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 = 7% of Principal
= 7% of $5100
= 7/100 × 5100
= 7 × 5100/100
= 35700/100 = 357
Thus, simple Interest for 1 year = $357
Now,
∵ If the simple Interest is $357, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/357 years
∴ If the simple Interest is $2142, then the time = 1/357 × 2142 years
= 1 × 2142/357 years
= 2142/357 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(3) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(7) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.