Question:
How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?
Correct Answer
$7400
Solution And Explanation
Solution
Given,
Amount (A) = $9250
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
$9250 = P (1 + 5% × 5)
⇒ $9250 = P (1 + 5/100 × 5)
⇒ $9250 = P (1 + 5 × 5/100)
⇒ $9250 = P (1 + 25/100)
⇒ $9250 = P (100 + 25/100)
⇒ $9250 = P × 125/100
⇒ P × 125/100 = $9250
⇒ P = 9250/125/100
⇒ P = 9250 × 100/125
⇒ P = 9250 × 100/125
⇒ P = 925000/125
⇒ P = $7400
Thus, the sum borrowed (P) = $7400 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 9250, then the Principal = 100/125 × 9250
= 100 × 9250/125
= 925000/125
= 7400
Thus, Principal = $7400
Thus, the sum borrowed = $7400 Answer
Similar Questions
(1) How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?
(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?
(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(6) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 8% simple interest?
(8) 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.
(9) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.