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 John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.
(3) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?
(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(7) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(9) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.