Question:
Andrew had to pay $5376 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
$4800
Solution And Explanation
Solution
Given,
Amount (A) = $5376
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
$5376 = P (1 + 4% × 3)
⇒ $5376 = P (1 + 4/100 × 3)
⇒ $5376 = P (1 + 4 × 3/100)
⇒ $5376 = P (1 + 12/100)
⇒ $5376 = P (100 + 12/100)
⇒ $5376 = P × 112/100
⇒ P × 112/100 = $5376
⇒ P = 5376/112/100
⇒ P = 5376 × 100/112
⇒ P = 5376 × 100/112
⇒ P = 537600/112
⇒ P = $4800
Thus, the sum borrowed (P) = $4800 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 5376, then the Principal = 100/112 × 5376
= 100 × 5376/112
= 537600/112
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(6) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.
(10) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?