Question:
Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$4350
Solution And Explanation
Solution
Given,
Amount (A) = $4741.5
Rate of Simple Interest (R) = 3%
Time (T) = 3 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
$4741.5 = P (1 + 3% × 3)
⇒ $4741.5 = P (1 + 3/100 × 3)
⇒ $4741.5 = P (1 + 3 × 3/100)
⇒ $4741.5 = P (1 + 9/100)
⇒ $4741.5 = P (100 + 9/100)
⇒ $4741.5 = P × 109/100
⇒ P × 109/100 = $4741.5
⇒ P = 4741.5/109/100
⇒ P = 4741.5 × 100/109
⇒ P = 4741.5 × 100/109
⇒ P = 474150/109
⇒ P = $4350
Thus, the sum borrowed (P) = $4350 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 4741.5, then the Principal = 100/109 × 4741.5
= 100 × 4741.5/109
= 474150/109
= 4350
Thus, Principal = $4350
Thus, the sum borrowed = $4350 Answer
Similar Questions
(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?
(2) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(4) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.
(6) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?
(8) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.