Question:
How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
Correct Answer
$6900
Solution And Explanation
Solution
Given,
Amount (A) = $8625
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
$8625 = P (1 + 5% × 5)
⇒ $8625 = P (1 + 5/100 × 5)
⇒ $8625 = P (1 + 5 × 5/100)
⇒ $8625 = P (1 + 25/100)
⇒ $8625 = P (100 + 25/100)
⇒ $8625 = P × 125/100
⇒ P × 125/100 = $8625
⇒ P = 8625/125/100
⇒ P = 8625 × 100/125
⇒ P = 8625 × 100/125
⇒ P = 862500/125
⇒ P = $6900
Thus, the sum borrowed (P) = $6900 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 8625, then the Principal = 100/125 × 8625
= 100 × 8625/125
= 862500/125
= 6900
Thus, Principal = $6900
Thus, the sum borrowed = $6900 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(2) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(6) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.
(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.
(9) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?