Question:
Nancy had to pay $4772.5 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
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4772.5
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
$4772.5 = P (1 + 5% × 3)
⇒ $4772.5 = P (1 + 5/100 × 3)
⇒ $4772.5 = P (1 + 5 × 3/100)
⇒ $4772.5 = P (1 + 15/100)
⇒ $4772.5 = P (100 + 15/100)
⇒ $4772.5 = P × 115/100
⇒ P × 115/100 = $4772.5
⇒ P = 4772.5/115/100
⇒ P = 4772.5 × 100/115
⇒ P = 4772.5 × 100/115
⇒ P = 477250/115
⇒ 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 = 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 4772.5, then the Principal = 100/115 × 4772.5
= 100 × 4772.5/115
= 477250/115
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(3) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?
(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(6) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(7) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(10) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?