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) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(4) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(5) Christopher had to pay $4360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(9) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?