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) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.
(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.
(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(8) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.