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) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 4 years.
(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(4) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(6) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?