Question:
How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?
Correct Answer
$6950
Solution And Explanation
Solution
Given,
Amount (A) = $8340
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
$8340 = P (1 + 4% × 5)
⇒ $8340 = P (1 + 4/100 × 5)
⇒ $8340 = P (1 + 4 × 5/100)
⇒ $8340 = P (1 + 20/100)
⇒ $8340 = P (100 + 20/100)
⇒ $8340 = P × 120/100
⇒ P × 120/100 = $8340
⇒ P = 8340/120/100
⇒ P = 8340 × 100/120
⇒ P = 8340 × 100/120
⇒ P = 834000/120
⇒ P = $6950
Thus, the sum borrowed (P) = $6950 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 8340, then the Principal = 100/120 × 8340
= 100 × 8340/120
= 834000/120
= 6950
Thus, Principal = $6950
Thus, the sum borrowed = $6950 Answer
Similar Questions
(1) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?
(2) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(5) Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(7) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.