Question:
Karen had to pay $4542.5 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
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4542.5
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
$4542.5 = P (1 + 5% × 3)
⇒ $4542.5 = P (1 + 5/100 × 3)
⇒ $4542.5 = P (1 + 5 × 3/100)
⇒ $4542.5 = P (1 + 15/100)
⇒ $4542.5 = P (100 + 15/100)
⇒ $4542.5 = P × 115/100
⇒ P × 115/100 = $4542.5
⇒ P = 4542.5/115/100
⇒ P = 4542.5 × 100/115
⇒ P = 4542.5 × 100/115
⇒ P = 454250/115
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 4542.5, then the Principal = 100/115 × 4542.5
= 100 × 4542.5/115
= 454250/115
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 3 years.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(7) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(10) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?