Question:
How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?
Correct Answer
$5400
Solution And Explanation
Solution
Given,
Amount (A) = $6750
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
$6750 = P (1 + 5% × 5)
⇒ $6750 = P (1 + 5/100 × 5)
⇒ $6750 = P (1 + 5 × 5/100)
⇒ $6750 = P (1 + 25/100)
⇒ $6750 = P (100 + 25/100)
⇒ $6750 = P × 125/100
⇒ P × 125/100 = $6750
⇒ P = 6750/125/100
⇒ P = 6750 × 100/125
⇒ P = 6750 × 100/125
⇒ P = 675000/125
⇒ P = $5400
Thus, the sum borrowed (P) = $5400 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 6750, then the Principal = 100/125 × 6750
= 100 × 6750/125
= 675000/125
= 5400
Thus, Principal = $5400
Thus, the sum borrowed = $5400 Answer
Similar Questions
(1) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.
(3) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.
(5) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?
(7) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?