Question:
Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$4650
Solution And Explanation
Solution
Given,
Amount (A) = $5347.5
Rate of Simple Interest (R) = 5%
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
$5347.5 = P (1 + 5% × 3)
⇒ $5347.5 = P (1 + 5/100 × 3)
⇒ $5347.5 = P (1 + 5 × 3/100)
⇒ $5347.5 = P (1 + 15/100)
⇒ $5347.5 = P (100 + 15/100)
⇒ $5347.5 = P × 115/100
⇒ P × 115/100 = $5347.5
⇒ P = 5347.5/115/100
⇒ P = 5347.5 × 100/115
⇒ P = 5347.5 × 100/115
⇒ P = 534750/115
⇒ P = $4650
Thus, the sum borrowed (P) = $4650 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 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 5347.5, then the Principal = 100/115 × 5347.5
= 100 × 5347.5/115
= 534750/115
= 4650
Thus, Principal = $4650
Thus, the sum borrowed = $4650 Answer
Similar Questions
(1) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(4) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
(7) 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.
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
(9) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.