Question:
How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Amount (A) = $8222.5
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
$8222.5 = P (1 + 3% × 5)
⇒ $8222.5 = P (1 + 3/100 × 5)
⇒ $8222.5 = P (1 + 3 × 5/100)
⇒ $8222.5 = P (1 + 15/100)
⇒ $8222.5 = P (100 + 15/100)
⇒ $8222.5 = P × 115/100
⇒ P × 115/100 = $8222.5
⇒ P = 8222.5/115/100
⇒ P = 8222.5 × 100/115
⇒ P = 8222.5 × 100/115
⇒ P = 822250/115
⇒ P = $7150
Thus, the sum borrowed (P) = $7150 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 8222.5, then the Principal = 100/115 × 8222.5
= 100 × 8222.5/115
= 822250/115
= 7150
Thus, Principal = $7150
Thus, the sum borrowed = $7150 Answer
Similar Questions
(1) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(2) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(3) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?
(6) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.
(8) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.