Question:
Barbara had to pay $4082.5 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
$3550
Solution And Explanation
Solution
Given,
Amount (A) = $4082.5
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
$4082.5 = P (1 + 5% × 3)
⇒ $4082.5 = P (1 + 5/100 × 3)
⇒ $4082.5 = P (1 + 5 × 3/100)
⇒ $4082.5 = P (1 + 15/100)
⇒ $4082.5 = P (100 + 15/100)
⇒ $4082.5 = P × 115/100
⇒ P × 115/100 = $4082.5
⇒ P = 4082.5/115/100
⇒ P = 4082.5 × 100/115
⇒ P = 4082.5 × 100/115
⇒ P = 408250/115
⇒ P = $3550
Thus, the sum borrowed (P) = $3550 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 4082.5, then the Principal = 100/115 × 4082.5
= 100 × 4082.5/115
= 408250/115
= 3550
Thus, Principal = $3550
Thus, the sum borrowed = $3550 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.
(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(4) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.
(8) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
(10) 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.