Question:
Sarah had to pay $4427.5 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
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4427.5
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
$4427.5 = P (1 + 5% × 3)
⇒ $4427.5 = P (1 + 5/100 × 3)
⇒ $4427.5 = P (1 + 5 × 3/100)
⇒ $4427.5 = P (1 + 15/100)
⇒ $4427.5 = P (100 + 15/100)
⇒ $4427.5 = P × 115/100
⇒ P × 115/100 = $4427.5
⇒ P = 4427.5/115/100
⇒ P = 4427.5 × 100/115
⇒ P = 4427.5 × 100/115
⇒ P = 442750/115
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 4427.5, then the Principal = 100/115 × 4427.5
= 100 × 4427.5/115
= 442750/115
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(2) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?
(3) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?
(7) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(10) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?