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) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(2) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
(8) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(10) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?