Question:
How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?
Correct Answer
$5350
Solution And Explanation
Solution
Given,
Amount (A) = $6152.5
Rate of Simple Interest (R) = 3%
Time (T) = 5 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
$6152.5 = P (1 + 3% × 5)
⇒ $6152.5 = P (1 + 3/100 × 5)
⇒ $6152.5 = P (1 + 3 × 5/100)
⇒ $6152.5 = P (1 + 15/100)
⇒ $6152.5 = P (100 + 15/100)
⇒ $6152.5 = P × 115/100
⇒ P × 115/100 = $6152.5
⇒ P = 6152.5/115/100
⇒ P = 6152.5 × 100/115
⇒ P = 6152.5 × 100/115
⇒ P = 615250/115
⇒ P = $5350
Thus, the sum borrowed (P) = $5350 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 3 = 15
Thus, simple interest for 5 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 6152.5, then the Principal = 100/115 × 6152.5
= 100 × 6152.5/115
= 615250/115
= 5350
Thus, Principal = $5350
Thus, the sum borrowed = $5350 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(4) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?
(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?
(9) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.