Question:
How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?
Correct Answer
$6200
Solution And Explanation
Solution
Given,
Amount (A) = $7750
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
$7750 = P (1 + 5% × 5)
⇒ $7750 = P (1 + 5/100 × 5)
⇒ $7750 = P (1 + 5 × 5/100)
⇒ $7750 = P (1 + 25/100)
⇒ $7750 = P (100 + 25/100)
⇒ $7750 = P × 125/100
⇒ P × 125/100 = $7750
⇒ P = 7750/125/100
⇒ P = 7750 × 100/125
⇒ P = 7750 × 100/125
⇒ P = 775000/125
⇒ P = $6200
Thus, the sum borrowed (P) = $6200 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 7750, then the Principal = 100/125 × 7750
= 100 × 7750/125
= 775000/125
= 6200
Thus, Principal = $6200
Thus, the sum borrowed = $6200 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(3) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(7) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(9) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.