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) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?
(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.
(5) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(7) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.
(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?