Question:
How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Amount (A) = $7620
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
$7620 = P (1 + 4% × 5)
⇒ $7620 = P (1 + 4/100 × 5)
⇒ $7620 = P (1 + 4 × 5/100)
⇒ $7620 = P (1 + 20/100)
⇒ $7620 = P (100 + 20/100)
⇒ $7620 = P × 120/100
⇒ P × 120/100 = $7620
⇒ P = 7620/120/100
⇒ P = 7620 × 100/120
⇒ P = 7620 × 100/120
⇒ P = 762000/120
⇒ P = $6350
Thus, the sum borrowed (P) = $6350 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 7620, then the Principal = 100/120 × 7620
= 100 × 7620/120
= 762000/120
= 6350
Thus, Principal = $6350
Thus, the sum borrowed = $6350 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(5) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.
(8) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.