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) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.
(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?
(3) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?
(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(8) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.
(10) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.