Question:
Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10921
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 = $10921 – $6700 = $4221
Thus, Simple Interest = $4221
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 × 4221/6700 × 7
= 422100/46900
= 9 years (using formula)
Thus, Time (T) = 9 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 = $4221 (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 $4221, then the time = 1/469 × 4221 years
= 1 × 4221/469 years
= 4221/469 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?
(3) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(4) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.
(7) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(9) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.