Question:
Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11247
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 = $11247 – $6900 = $4347
Thus, Simple Interest = $4347
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 × 4347/6900 × 9
= 434700/62100
= 7 years (using formula)
Thus, Time (T) = 7 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) = $6900
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4347 (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 $6900
= 9/100 × 6900
= 9 × 6900/100
= 62100/100 = 621
Thus, simple Interest for 1 year = $621
Now,
∵ If the simple Interest is $621, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/621 years
∴ If the simple Interest is $4347, then the time = 1/621 × 4347 years
= 1 × 4347/621 years
= 4347/621 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(2) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
(3) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.
(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
(6) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?
(7) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(10) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?