Question:
Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9514
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 = $9514 – $6700 = $2814
Thus, Simple Interest = $2814
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 × 2814/6700 × 7
= 281400/46900
= 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) = $6700
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2814 (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 $6700
= 7/100 × 6700
= 7 × 6700/100
= 46900/100 = 469
Thus, simple Interest for 1 year = $469
Now,
∵ If the simple Interest is $469, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/469 years
∴ If the simple Interest is $2814, then the time = 1/469 × 2814 years
= 1 × 2814/469 years
= 2814/469 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(2) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.
(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(6) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(8) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.