Question:
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.
Correct Answer
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4485
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
$4485 = P (1 + 5% × 3)
⇒ $4485 = P (1 + 5/100 × 3)
⇒ $4485 = P (1 + 5 × 3/100)
⇒ $4485 = P (1 + 15/100)
⇒ $4485 = P (100 + 15/100)
⇒ $4485 = P × 115/100
⇒ P × 115/100 = $4485
⇒ P = 4485/115/100
⇒ P = 4485 × 100/115
⇒ P = 4485 × 100/115
⇒ P = 448500/115
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 4485, then the Principal = 100/115 × 4485
= 100 × 4485/115
= 448500/115
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.
(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(6) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(9) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?