Question:
Jessica had to pay $4087.5 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
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $4087.5
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
$4087.5 = P (1 + 3% × 3)
⇒ $4087.5 = P (1 + 3/100 × 3)
⇒ $4087.5 = P (1 + 3 × 3/100)
⇒ $4087.5 = P (1 + 9/100)
⇒ $4087.5 = P (100 + 9/100)
⇒ $4087.5 = P × 109/100
⇒ P × 109/100 = $4087.5
⇒ P = 4087.5/109/100
⇒ P = 4087.5 × 100/109
⇒ P = 4087.5 × 100/109
⇒ P = 408750/109
⇒ P = $3750
Thus, the sum borrowed (P) = $3750 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 4087.5, then the Principal = 100/109 × 4087.5
= 100 × 4087.5/109
= 408750/109
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(5) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?
(7) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(8) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.