Question:
Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6700
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $12730
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 = $12730 – $6700 = $6030
Thus, Simple Interest = $6030
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 × 6030/6700 × 9
= 603000/60300
= 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) = $6700
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $6030 (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 = 9% of Principal
= 9% of $6700
= 9/100 × 6700
= 9 × 6700/100
= 60300/100 = 603
Thus, simple Interest for 1 year = $603
Now,
∵ If the simple Interest is $603, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/603 years
∴ If the simple Interest is $6030, then the time = 1/603 × 6030 years
= 1 × 6030/603 years
= 6030/603 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(2) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(4) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
(5) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(6) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.
(9) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.