Question : Sandra had to pay $5117.5 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 $4450
Solution & Explanation
Solution
Given,
Amount (A) = $5117.5
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
$5117.5 = P (1 + 5% × 3)
⇒ $5117.5 = P (1 + 5/100 × 3)
⇒ $5117.5 = P (1 + 5 × 3/100)
⇒ $5117.5 = P (1 + 15/100)
⇒ $5117.5 = P (100 + 15/100)
⇒ $5117.5 = P × 115/100
⇒ P × 115/100 = $5117.5
⇒ P = 5117.5/115/100
⇒ P = 5117.5 × 100/115
⇒ P = 5117.5 × 100/115
⇒ P = 511750/115
⇒ P = $4450
Thus, the sum borrowed (P) = $4450 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 5117.5, then the Principal = 100/115 × 5117.5
= 100 × 5117.5/115
= 511750/115
= 4450
Thus, Principal = $4450
Thus, the sum borrowed = $4450 Answer
Similar Questions
(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 4% simple interest?
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?
(8) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?