Question:
Jessica had to pay $4312.5 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
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $4312.5
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
$4312.5 = P (1 + 5% × 3)
⇒ $4312.5 = P (1 + 5/100 × 3)
⇒ $4312.5 = P (1 + 5 × 3/100)
⇒ $4312.5 = P (1 + 15/100)
⇒ $4312.5 = P (100 + 15/100)
⇒ $4312.5 = P × 115/100
⇒ P × 115/100 = $4312.5
⇒ P = 4312.5/115/100
⇒ P = 4312.5 × 100/115
⇒ P = 4312.5 × 100/115
⇒ P = 431250/115
⇒ P = $3750
Thus, the sum borrowed (P) = $3750 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 4312.5, then the Principal = 100/115 × 4312.5
= 100 × 4312.5/115
= 431250/115
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 Answer
Similar Questions
(1) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?
(3) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(4) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.