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 Charles borrowed a sum of $3900 at 5% simple interest for 4 years.
(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(3) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?
(5) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(10) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.