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) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
(2) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(4) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
(6) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?
(9) 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.
(10) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.