Question : Robert had to pay $3565 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 $3100
Solution & Explanation
Solution
Given,
Amount (A) = $3565
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
$3565 = P (1 + 5% × 3)
⇒ $3565 = P (1 + 5/100 × 3)
⇒ $3565 = P (1 + 5 × 3/100)
⇒ $3565 = P (1 + 15/100)
⇒ $3565 = P (100 + 15/100)
⇒ $3565 = P × 115/100
⇒ P × 115/100 = $3565
⇒ P = 3565/115/100
⇒ P = 3565 × 100/115
⇒ P = 3565 × 100/115
⇒ P = 356500/115
⇒ P = $3100
Thus, the sum borrowed (P) = $3100 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 3565, then the Principal = 100/115 × 3565
= 100 × 3565/115
= 356500/115
= 3100
Thus, Principal = $3100
Thus, the sum borrowed = $3100 Answer
Similar Questions
(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.
(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.
(6) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?