Question:
Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4100
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $6970
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 = $6970 – $4100 = $2870
Thus, Simple Interest = $2870
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 × 2870/4100 × 7
= 287000/28700
= 10 years (using formula)
Thus, Time (T) = 10 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) = $4100
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2870 (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 $4100
= 7/100 × 4100
= 7 × 4100/100
= 28700/100 = 287
Thus, simple Interest for 1 year = $287
Now,
∵ If the simple Interest is $287, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/287 years
∴ If the simple Interest is $2870, then the time = 1/287 × 2870 years
= 1 × 2870/287 years
= 2870/287 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(2) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(5) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(7) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
(8) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(9) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.