Question:
Anthony had to pay $4945 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
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4945
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
$4945 = P (1 + 5% × 3)
⇒ $4945 = P (1 + 5/100 × 3)
⇒ $4945 = P (1 + 5 × 3/100)
⇒ $4945 = P (1 + 15/100)
⇒ $4945 = P (100 + 15/100)
⇒ $4945 = P × 115/100
⇒ P × 115/100 = $4945
⇒ P = 4945/115/100
⇒ P = 4945 × 100/115
⇒ P = 4945 × 100/115
⇒ P = 494500/115
⇒ P = $4300
Thus, the sum borrowed (P) = $4300 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 4945, then the Principal = 100/115 × 4945
= 100 × 4945/115
= 494500/115
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(2) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(4) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
(5) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?
(7) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?
(9) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?
(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.