Question:
Betty had to pay $4887.5 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
$4250
Solution And Explanation
Solution
Given,
Amount (A) = $4887.5
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
$4887.5 = P (1 + 5% × 3)
⇒ $4887.5 = P (1 + 5/100 × 3)
⇒ $4887.5 = P (1 + 5 × 3/100)
⇒ $4887.5 = P (1 + 15/100)
⇒ $4887.5 = P (100 + 15/100)
⇒ $4887.5 = P × 115/100
⇒ P × 115/100 = $4887.5
⇒ P = 4887.5/115/100
⇒ P = 4887.5 × 100/115
⇒ P = 4887.5 × 100/115
⇒ P = 488750/115
⇒ P = $4250
Thus, the sum borrowed (P) = $4250 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 4887.5, then the Principal = 100/115 × 4887.5
= 100 × 4887.5/115
= 488750/115
= 4250
Thus, Principal = $4250
Thus, the sum borrowed = $4250 Answer
Similar Questions
(1) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?
(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(7) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
(9) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.