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) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(2) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
(5) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(6) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(8) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(9) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.