Question:
How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?
Correct Answer
$7350
Solution And Explanation
Solution
Given,
Amount (A) = $8820
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
$8820 = P (1 + 4% × 5)
⇒ $8820 = P (1 + 4/100 × 5)
⇒ $8820 = P (1 + 4 × 5/100)
⇒ $8820 = P (1 + 20/100)
⇒ $8820 = P (100 + 20/100)
⇒ $8820 = P × 120/100
⇒ P × 120/100 = $8820
⇒ P = 8820/120/100
⇒ P = 8820 × 100/120
⇒ P = 8820 × 100/120
⇒ P = 882000/120
⇒ P = $7350
Thus, the sum borrowed (P) = $7350 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 8820, then the Principal = 100/120 × 8820
= 100 × 8820/120
= 882000/120
= 7350
Thus, Principal = $7350
Thus, the sum borrowed = $7350 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(2) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.
(4) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(6) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(7) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
(8) 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?
(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(10) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.