Question:
How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
Correct Answer
$5650
Solution And Explanation
Solution
Given,
Amount (A) = $6497.5
Rate of Simple Interest (R) = 3%
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
$6497.5 = P (1 + 3% × 5)
⇒ $6497.5 = P (1 + 3/100 × 5)
⇒ $6497.5 = P (1 + 3 × 5/100)
⇒ $6497.5 = P (1 + 15/100)
⇒ $6497.5 = P (100 + 15/100)
⇒ $6497.5 = P × 115/100
⇒ P × 115/100 = $6497.5
⇒ P = 6497.5/115/100
⇒ P = 6497.5 × 100/115
⇒ P = 6497.5 × 100/115
⇒ P = 649750/115
⇒ P = $5650
Thus, the sum borrowed (P) = $5650 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6497.5, then the Principal = 100/115 × 6497.5
= 100 × 6497.5/115
= 649750/115
= 5650
Thus, Principal = $5650
Thus, the sum borrowed = $5650 Answer
Similar Questions
(1) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.
(4) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?
(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?
(6) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(8) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?
(9) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.
(10) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.