Question : Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer $4850
Solution & Explanation
Solution
Given,
Amount (A) = $5286.5
Rate of Simple Interest (R) = 3%
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
$5286.5 = P (1 + 3% × 3)
⇒ $5286.5 = P (1 + 3/100 × 3)
⇒ $5286.5 = P (1 + 3 × 3/100)
⇒ $5286.5 = P (1 + 9/100)
⇒ $5286.5 = P (100 + 9/100)
⇒ $5286.5 = P × 109/100
⇒ P × 109/100 = $5286.5
⇒ P = 5286.5/109/100
⇒ P = 5286.5 × 100/109
⇒ P = 5286.5 × 100/109
⇒ P = 528650/109
⇒ P = $4850
Thus, the sum borrowed (P) = $4850 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 5286.5, then the Principal = 100/109 × 5286.5
= 100 × 5286.5/109
= 528650/109
= 4850
Thus, Principal = $4850
Thus, the sum borrowed = $4850 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(2) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?