Question:
How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?
Correct Answer
$6550
Solution And Explanation
Solution
Given,
Amount (A) = $8187.5
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
$8187.5 = P (1 + 5% × 5)
⇒ $8187.5 = P (1 + 5/100 × 5)
⇒ $8187.5 = P (1 + 5 × 5/100)
⇒ $8187.5 = P (1 + 25/100)
⇒ $8187.5 = P (100 + 25/100)
⇒ $8187.5 = P × 125/100
⇒ P × 125/100 = $8187.5
⇒ P = 8187.5/125/100
⇒ P = 8187.5 × 100/125
⇒ P = 8187.5 × 100/125
⇒ P = 818750/125
⇒ P = $6550
Thus, the sum borrowed (P) = $6550 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 8187.5, then the Principal = 100/125 × 8187.5
= 100 × 8187.5/125
= 818750/125
= 6550
Thus, Principal = $6550
Thus, the sum borrowed = $6550 Answer
Similar Questions
(1) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(2) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.
(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 4% simple interest?
(4) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(5) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?
(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.