Question:
How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
Correct Answer
$5750
Solution And Explanation
Solution
Given,
Amount (A) = $6612.5
Rate of Simple Interest (R) = 3%
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
$6612.5 = P (1 + 3% × 5)
⇒ $6612.5 = P (1 + 3/100 × 5)
⇒ $6612.5 = P (1 + 3 × 5/100)
⇒ $6612.5 = P (1 + 15/100)
⇒ $6612.5 = P (100 + 15/100)
⇒ $6612.5 = P × 115/100
⇒ P × 115/100 = $6612.5
⇒ P = 6612.5/115/100
⇒ P = 6612.5 × 100/115
⇒ P = 6612.5 × 100/115
⇒ P = 661250/115
⇒ P = $5750
Thus, the sum borrowed (P) = $5750 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6612.5, then the Principal = 100/115 × 6612.5
= 100 × 6612.5/115
= 661250/115
= 5750
Thus, Principal = $5750
Thus, the sum borrowed = $5750 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?
(2) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(4) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.
(8) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Christopher had to pay $4360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?