Question:
How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
Correct Answer
$6700
Solution And Explanation
Solution
Given,
Amount (A) = $8040
Rate of Simple Interest (R) = 4%
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
$8040 = P (1 + 4% × 5)
⇒ $8040 = P (1 + 4/100 × 5)
⇒ $8040 = P (1 + 4 × 5/100)
⇒ $8040 = P (1 + 20/100)
⇒ $8040 = P (100 + 20/100)
⇒ $8040 = P × 120/100
⇒ P × 120/100 = $8040
⇒ P = 8040/120/100
⇒ P = 8040 × 100/120
⇒ P = 8040 × 100/120
⇒ P = 804000/120
⇒ P = $6700
Thus, the sum borrowed (P) = $6700 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 8040, then the Principal = 100/120 × 8040
= 100 × 8040/120
= 804000/120
= 6700
Thus, Principal = $6700
Thus, the sum borrowed = $6700 Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(4) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?
(6) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(7) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(8) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.