Question:
How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?
Correct Answer
$6750
Solution And Explanation
Solution
Given,
Amount (A) = $8437.5
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
$8437.5 = P (1 + 5% × 5)
⇒ $8437.5 = P (1 + 5/100 × 5)
⇒ $8437.5 = P (1 + 5 × 5/100)
⇒ $8437.5 = P (1 + 25/100)
⇒ $8437.5 = P (100 + 25/100)
⇒ $8437.5 = P × 125/100
⇒ P × 125/100 = $8437.5
⇒ P = 8437.5/125/100
⇒ P = 8437.5 × 100/125
⇒ P = 8437.5 × 100/125
⇒ P = 843750/125
⇒ P = $6750
Thus, the sum borrowed (P) = $6750 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 8437.5, then the Principal = 100/125 × 8437.5
= 100 × 8437.5/125
= 843750/125
= 6750
Thus, Principal = $6750
Thus, the sum borrowed = $6750 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(3) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
(4) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(8) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
(9) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(10) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.