Question:
John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 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) = 10% per annum
Amount (A) = $8360
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 = $8360 – $4400 = $3960
Thus, Simple Interest = $3960
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 × 3960/4400 × 10
= 396000/44000
= 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) = 10% per annum
Simple Interest = $3960 (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 = 10% of Principal
= 10% of $4400
= 10/100 × 4400
= 10 × 4400/100
= 44000/100 = 440
Thus, simple Interest for 1 year = $440
Now,
∵ If the simple Interest is $440, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/440 years
∴ If the simple Interest is $3960, then the time = 1/440 × 3960 years
= 1 × 3960/440 years
= 3960/440 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?