Question:
Andrew had to pay $5520 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
$4800
Solution And Explanation
Solution
Given,
Amount (A) = $5520
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
$5520 = P (1 + 5% × 3)
⇒ $5520 = P (1 + 5/100 × 3)
⇒ $5520 = P (1 + 5 × 3/100)
⇒ $5520 = P (1 + 15/100)
⇒ $5520 = P (100 + 15/100)
⇒ $5520 = P × 115/100
⇒ P × 115/100 = $5520
⇒ P = 5520/115/100
⇒ P = 5520 × 100/115
⇒ P = 5520 × 100/115
⇒ P = 552000/115
⇒ 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 = 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 5520, then the Principal = 100/115 × 5520
= 100 × 5520/115
= 552000/115
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(4) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(5) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(8) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.