Question:
Nancy had to pay $4523.5 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
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4523.5
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
$4523.5 = P (1 + 3% × 3)
⇒ $4523.5 = P (1 + 3/100 × 3)
⇒ $4523.5 = P (1 + 3 × 3/100)
⇒ $4523.5 = P (1 + 9/100)
⇒ $4523.5 = P (100 + 9/100)
⇒ $4523.5 = P × 109/100
⇒ P × 109/100 = $4523.5
⇒ P = 4523.5/109/100
⇒ P = 4523.5 × 100/109
⇒ P = 4523.5 × 100/109
⇒ P = 452350/109
⇒ P = $4150
Thus, the sum borrowed (P) = $4150 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 4523.5, then the Principal = 100/109 × 4523.5
= 100 × 4523.5/109
= 452350/109
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(3) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?
(5) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(6) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(8) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(9) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.