Question:
How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
Correct Answer
$7850
Solution And Explanation
Solution
Given,
Amount (A) = $9812.5
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
$9812.5 = P (1 + 5% × 5)
⇒ $9812.5 = P (1 + 5/100 × 5)
⇒ $9812.5 = P (1 + 5 × 5/100)
⇒ $9812.5 = P (1 + 25/100)
⇒ $9812.5 = P (100 + 25/100)
⇒ $9812.5 = P × 125/100
⇒ P × 125/100 = $9812.5
⇒ P = 9812.5/125/100
⇒ P = 9812.5 × 100/125
⇒ P = 9812.5 × 100/125
⇒ P = 981250/125
⇒ P = $7850
Thus, the sum borrowed (P) = $7850 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 9812.5, then the Principal = 100/125 × 9812.5
= 100 × 9812.5/125
= 981250/125
= 7850
Thus, Principal = $7850
Thus, the sum borrowed = $7850 Answer
Similar Questions
(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.
(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 6% simple interest?
(7) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(10) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.