Question:
John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 6% 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 × 6
= 237600/26400
= 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) = $4400
Rate of Simple Interest (R) = 6% 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 = 6% of Principal
= 6% of $4400
= 6/100 × 4400
= 6 × 4400/100
= 26400/100 = 264
Thus, simple Interest for 1 year = $264
Now,
∵ If the simple Interest is $264, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/264 years
∴ If the simple Interest is $2376, then the time = 1/264 × 2376 years
= 1 × 2376/264 years
= 2376/264 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.
(2) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(3) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.
(6) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.
(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.