Question:
Paul had to pay $5405 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
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $5405
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
$5405 = P (1 + 5% × 3)
⇒ $5405 = P (1 + 5/100 × 3)
⇒ $5405 = P (1 + 5 × 3/100)
⇒ $5405 = P (1 + 15/100)
⇒ $5405 = P (100 + 15/100)
⇒ $5405 = P × 115/100
⇒ P × 115/100 = $5405
⇒ P = 5405/115/100
⇒ P = 5405 × 100/115
⇒ P = 5405 × 100/115
⇒ P = 540500/115
⇒ P = $4700
Thus, the sum borrowed (P) = $4700 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 5405, then the Principal = 100/115 × 5405
= 100 × 5405/115
= 540500/115
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.
(2) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $7752 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.
(4) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(6) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?
(8) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?
(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.