Question:
Jessica had to pay $4312.5 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
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $4312.5
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
$4312.5 = P (1 + 5% × 3)
⇒ $4312.5 = P (1 + 5/100 × 3)
⇒ $4312.5 = P (1 + 5 × 3/100)
⇒ $4312.5 = P (1 + 15/100)
⇒ $4312.5 = P (100 + 15/100)
⇒ $4312.5 = P × 115/100
⇒ P × 115/100 = $4312.5
⇒ P = 4312.5/115/100
⇒ P = 4312.5 × 100/115
⇒ P = 4312.5 × 100/115
⇒ P = 431250/115
⇒ 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 = 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 4312.5, then the Principal = 100/115 × 4312.5
= 100 × 4312.5/115
= 431250/115
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 Answer
Similar Questions
(1) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(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) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(10) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.