Question:
Lisa had to pay $4293 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
$4050
Solution And Explanation
Solution
Given,
Amount (A) = $4293
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
$4293 = P (1 + 2% × 3)
⇒ $4293 = P (1 + 2/100 × 3)
⇒ $4293 = P (1 + 2 × 3/100)
⇒ $4293 = P (1 + 6/100)
⇒ $4293 = P (100 + 6/100)
⇒ $4293 = P × 106/100
⇒ P × 106/100 = $4293
⇒ P = 4293/106/100
⇒ P = 4293 × 100/106
⇒ P = 4293 × 100/106
⇒ P = 429300/106
⇒ P = $4050
Thus, the sum borrowed (P) = $4050 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 4293, then the Principal = 100/106 × 4293
= 100 × 4293/106
= 429300/106
= 4050
Thus, Principal = $4050
Thus, the sum borrowed = $4050 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?
(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 8% simple interest?
(4) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.
(7) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.
(10) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.