Question:
How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?
Correct Answer
$5300
Solution And Explanation
Solution
Given,
Amount (A) = $5830
Rate of Simple Interest (R) = 2%
Time (T) = 5 years
Thus, Principal (P) = ?
Method (1) Using Formula
Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given
Formula to find the Principal (P)
Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)
⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]
⇒ A = P (1 + RT)
Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given
In the given question, we need to find the Principal (P)
Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get
$5830 = P (1 + 2% × 5)
⇒ $5830 = P (1 + 2/100 × 5)
⇒ $5830 = P (1 + 2 × 5/100)
⇒ $5830 = P (1 + 10/100)
⇒ $5830 = P (100 + 10/100)
⇒ $5830 = P × 110/100
⇒ P × 110/100 = $5830
⇒ P = 5830/110/100
⇒ P = 5830 × 100/110
⇒ P = 5830 × 100/110
⇒ P = 583000/110
⇒ P = $5300
Thus, the sum borrowed (P) = $5300 Answer
Method (1) Using Unitary Method
Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given
Calculation of the Simple Interest
Let, the principal = 100
Here, since rate of simple interest = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5830, then the Principal = 100/110 × 5830
= 100 × 5830/110
= 583000/110
= 5300
Thus, Principal = $5300
Thus, the sum borrowed = $5300 Answer
Similar Questions
(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?
(3) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(4) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?
(8) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
(9) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?
(10) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?