Question:
Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$3150
Solution And Explanation
Solution
Given,
Amount (A) = $3528
Rate of Simple Interest (R) = 4%
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
$3528 = P (1 + 4% × 3)
⇒ $3528 = P (1 + 4/100 × 3)
⇒ $3528 = P (1 + 4 × 3/100)
⇒ $3528 = P (1 + 12/100)
⇒ $3528 = P (100 + 12/100)
⇒ $3528 = P × 112/100
⇒ P × 112/100 = $3528
⇒ P = 3528/112/100
⇒ P = 3528 × 100/112
⇒ P = 3528 × 100/112
⇒ P = 352800/112
⇒ P = $3150
Thus, the sum borrowed (P) = $3150 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 12
Thus, simple interest for 3 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 3528, then the Principal = 100/112 × 3528
= 100 × 3528/112
= 352800/112
= 3150
Thus, Principal = $3150
Thus, the sum borrowed = $3150 Answer
Similar Questions
(1) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.
(4) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?
(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(7) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(9) 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?
(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.