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 And 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) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.
(8) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?
(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(10) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.