Question:
Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$3350
Solution And Explanation
Solution
Given,
Amount (A) = $3852.5
Rate of Simple Interest (R) = 5%
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
$3852.5 = P (1 + 5% × 3)
⇒ $3852.5 = P (1 + 5/100 × 3)
⇒ $3852.5 = P (1 + 5 × 3/100)
⇒ $3852.5 = P (1 + 15/100)
⇒ $3852.5 = P (100 + 15/100)
⇒ $3852.5 = P × 115/100
⇒ P × 115/100 = $3852.5
⇒ P = 3852.5/115/100
⇒ P = 3852.5 × 100/115
⇒ P = 3852.5 × 100/115
⇒ P = 385250/115
⇒ P = $3350
Thus, the sum borrowed (P) = $3350 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 3852.5, then the Principal = 100/115 × 3852.5
= 100 × 3852.5/115
= 385250/115
= 3350
Thus, Principal = $3350
Thus, the sum borrowed = $3350 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(3) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(7) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(9) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.