Question:
John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7568
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 = $7568 – $4400 = $3168
Thus, Simple Interest = $3168
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 × 3168/4400 × 9
= 316800/39600
= 8 years (using formula)
Thus, Time (T) = 8 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 = $3168 (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 $3168, then the time = 1/396 × 3168 years
= 1 × 3168/396 years
= 3168/396 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?
(2) Donna had to pay $5432 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 Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(5) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?
(6) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(7) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(9) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.