Question:
How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?
Correct Answer
$5150
Solution And Explanation
Solution
Given,
Amount (A) = $6437.5
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
$6437.5 = P (1 + 5% × 5)
⇒ $6437.5 = P (1 + 5/100 × 5)
⇒ $6437.5 = P (1 + 5 × 5/100)
⇒ $6437.5 = P (1 + 25/100)
⇒ $6437.5 = P (100 + 25/100)
⇒ $6437.5 = P × 125/100
⇒ P × 125/100 = $6437.5
⇒ P = 6437.5/125/100
⇒ P = 6437.5 × 100/125
⇒ P = 6437.5 × 100/125
⇒ P = 643750/125
⇒ P = $5150
Thus, the sum borrowed (P) = $5150 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 6437.5, then the Principal = 100/125 × 6437.5
= 100 × 6437.5/125
= 643750/125
= 5150
Thus, Principal = $5150
Thus, the sum borrowed = $5150 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(8) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?
(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(10) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.