Question:
How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
Correct Answer
$5350
Solution And Explanation
Solution
Given,
Amount (A) = $6687.5
Rate of Simple Interest (R) = 5%
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
$6687.5 = P (1 + 5% × 5)
⇒ $6687.5 = P (1 + 5/100 × 5)
⇒ $6687.5 = P (1 + 5 × 5/100)
⇒ $6687.5 = P (1 + 25/100)
⇒ $6687.5 = P (100 + 25/100)
⇒ $6687.5 = P × 125/100
⇒ P × 125/100 = $6687.5
⇒ P = 6687.5/125/100
⇒ P = 6687.5 × 100/125
⇒ P = 6687.5 × 100/125
⇒ P = 668750/125
⇒ 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 = 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 = 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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 6687.5, then the Principal = 100/125 × 6687.5
= 100 × 6687.5/125
= 668750/125
= 5350
Thus, Principal = $5350
Thus, the sum borrowed = $5350 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.
(4) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?
(7) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(9) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?