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) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(2) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(4) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(6) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(7) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.