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) 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.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?
(4) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(6) What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(9) If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.