Question:
Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4550
Solution And Explanation
Solution
Given,
Amount (A) = $4823
Rate of Simple Interest (R) = 2%
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
$4823 = P (1 + 2% × 3)
⇒ $4823 = P (1 + 2/100 × 3)
⇒ $4823 = P (1 + 2 × 3/100)
⇒ $4823 = P (1 + 6/100)
⇒ $4823 = P (100 + 6/100)
⇒ $4823 = P × 106/100
⇒ P × 106/100 = $4823
⇒ P = 4823/106/100
⇒ P = 4823 × 100/106
⇒ P = 4823 × 100/106
⇒ P = 482300/106
⇒ P = $4550
Thus, the sum borrowed (P) = $4550 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4823, then the Principal = 100/106 × 4823
= 100 × 4823/106
= 482300/106
= 4550
Thus, Principal = $4550
Thus, the sum borrowed = $4550 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(3) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(6) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.