Question:
How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Amount (A) = $7302.5
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
$7302.5 = P (1 + 3% × 5)
⇒ $7302.5 = P (1 + 3/100 × 5)
⇒ $7302.5 = P (1 + 3 × 5/100)
⇒ $7302.5 = P (1 + 15/100)
⇒ $7302.5 = P (100 + 15/100)
⇒ $7302.5 = P × 115/100
⇒ P × 115/100 = $7302.5
⇒ P = 7302.5/115/100
⇒ P = 7302.5 × 100/115
⇒ P = 7302.5 × 100/115
⇒ P = 730250/115
⇒ P = $6350
Thus, the sum borrowed (P) = $6350 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 7302.5, then the Principal = 100/115 × 7302.5
= 100 × 7302.5/115
= 730250/115
= 6350
Thus, Principal = $6350
Thus, the sum borrowed = $6350 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 4% simple interest?
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.
(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?
(4) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?
(5) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 8 years.
(6) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(8) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.