Question:
How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
Correct Answer
$7050
Solution And Explanation
Solution
Given,
Amount (A) = $8460
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
$8460 = P (1 + 4% × 5)
⇒ $8460 = P (1 + 4/100 × 5)
⇒ $8460 = P (1 + 4 × 5/100)
⇒ $8460 = P (1 + 20/100)
⇒ $8460 = P (100 + 20/100)
⇒ $8460 = P × 120/100
⇒ P × 120/100 = $8460
⇒ P = 8460/120/100
⇒ P = 8460 × 100/120
⇒ P = 8460 × 100/120
⇒ P = 846000/120
⇒ P = $7050
Thus, the sum borrowed (P) = $7050 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 8460, then the Principal = 100/120 × 8460
= 100 × 8460/120
= 846000/120
= 7050
Thus, Principal = $7050
Thus, the sum borrowed = $7050 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(2) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(4) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(5) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?
(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?