Question:
Sandra had to pay $4717 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
$4450
Solution And Explanation
Solution
Given,
Amount (A) = $4717
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
$4717 = P (1 + 2% × 3)
⇒ $4717 = P (1 + 2/100 × 3)
⇒ $4717 = P (1 + 2 × 3/100)
⇒ $4717 = P (1 + 6/100)
⇒ $4717 = P (100 + 6/100)
⇒ $4717 = P × 106/100
⇒ P × 106/100 = $4717
⇒ P = 4717/106/100
⇒ P = 4717 × 100/106
⇒ P = 4717 × 100/106
⇒ P = 471700/106
⇒ P = $4450
Thus, the sum borrowed (P) = $4450 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 4717, then the Principal = 100/106 × 4717
= 100 × 4717/106
= 471700/106
= 4450
Thus, Principal = $4450
Thus, the sum borrowed = $4450 Answer
Similar Questions
(1) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(2) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(6) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(7) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(8) 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.
(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.