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) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?
(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?
(3) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(6) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(7) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.