Question:
Emily had to pay $5462.5 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
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5462.5
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
$5462.5 = P (1 + 5% × 3)
⇒ $5462.5 = P (1 + 5/100 × 3)
⇒ $5462.5 = P (1 + 5 × 3/100)
⇒ $5462.5 = P (1 + 15/100)
⇒ $5462.5 = P (100 + 15/100)
⇒ $5462.5 = P × 115/100
⇒ P × 115/100 = $5462.5
⇒ P = 5462.5/115/100
⇒ P = 5462.5 × 100/115
⇒ P = 5462.5 × 100/115
⇒ P = 546250/115
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 5462.5, then the Principal = 100/115 × 5462.5
= 100 × 5462.5/115
= 546250/115
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(2) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.
(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(7) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 5% simple interest?
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.