Question:
Kimberly had to pay $5068.5 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
$4650
Solution And Explanation
Solution
Given,
Amount (A) = $5068.5
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
$5068.5 = P (1 + 3% × 3)
⇒ $5068.5 = P (1 + 3/100 × 3)
⇒ $5068.5 = P (1 + 3 × 3/100)
⇒ $5068.5 = P (1 + 9/100)
⇒ $5068.5 = P (100 + 9/100)
⇒ $5068.5 = P × 109/100
⇒ P × 109/100 = $5068.5
⇒ P = 5068.5/109/100
⇒ P = 5068.5 × 100/109
⇒ P = 5068.5 × 100/109
⇒ P = 506850/109
⇒ P = $4650
Thus, the sum borrowed (P) = $4650 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 5068.5, then the Principal = 100/109 × 5068.5
= 100 × 5068.5/109
= 506850/109
= 4650
Thus, Principal = $4650
Thus, the sum borrowed = $4650 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.
(2) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(3) Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?
(8) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.
(10) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.