Question:
How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?
Correct Answer
$5250
Solution And Explanation
Solution
Given,
Amount (A) = $6562.5
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
$6562.5 = P (1 + 5% × 5)
⇒ $6562.5 = P (1 + 5/100 × 5)
⇒ $6562.5 = P (1 + 5 × 5/100)
⇒ $6562.5 = P (1 + 25/100)
⇒ $6562.5 = P (100 + 25/100)
⇒ $6562.5 = P × 125/100
⇒ P × 125/100 = $6562.5
⇒ P = 6562.5/125/100
⇒ P = 6562.5 × 100/125
⇒ P = 6562.5 × 100/125
⇒ P = 656250/125
⇒ P = $5250
Thus, the sum borrowed (P) = $5250 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 6562.5, then the Principal = 100/125 × 6562.5
= 100 × 6562.5/125
= 656250/125
= 5250
Thus, Principal = $5250
Thus, the sum borrowed = $5250 Answer
Similar Questions
(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(4) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(8) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?
(9) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.
(10) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.