Question:
( 1 of 10 ) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
9
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $6776
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 = $6776 – $4400 = $2376
Thus, Simple Interest = $2376
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 × 2376/4400 × 9
= 237600/39600
= 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) = $4400
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $2376 (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 $4400
= 9/100 × 4400
= 9 × 4400/100
= 39600/100 = 396
Thus, simple Interest for 1 year = $396
Now,
∵ If the simple Interest is $396, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/396 years
∴ If the simple Interest is $2376, then the time = 1/396 × 2376 years
= 1 × 2376/396 years
= 2376/396 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(2) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(3) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(5) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(6) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.