Question:
Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8316
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 = $8316 – $5400 = $2916
Thus, Simple Interest = $2916
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 × 2916/5400 × 9
= 291600/48600
= 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) = $5400
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $2916 (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 $5400
= 9/100 × 5400
= 9 × 5400/100
= 48600/100 = 486
Thus, simple Interest for 1 year = $486
Now,
∵ If the simple Interest is $486, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/486 years
∴ If the simple Interest is $2916, then the time = 1/486 × 2916 years
= 1 × 2916/486 years
= 2916/486 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(3) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(4) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.
(6) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?
(7) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
(10) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?