Question:
John took a loan of $4400 at the rate of 8% 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
9
Solution And Explanation
Solution
Given,
Principal (P) = $4400
Rate of Simple Interest (R) = 8% 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 × 8
= 316800/35200
= 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) = 8% 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 = 8% of Principal
= 8% of $4400
= 8/100 × 4400
= 8 × 4400/100
= 35200/100 = 352
Thus, simple Interest for 1 year = $352
Now,
∵ If the simple Interest is $352, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/352 years
∴ If the simple Interest is $3168, then the time = 1/352 × 3168 years
= 1 × 3168/352 years
= 3168/352 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(2) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.
(7) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.
(9) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.