Question:
How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
Correct Answer
$5550
Solution And Explanation
Solution
Given,
Amount (A) = $6660
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
$6660 = P (1 + 4% × 5)
⇒ $6660 = P (1 + 4/100 × 5)
⇒ $6660 = P (1 + 4 × 5/100)
⇒ $6660 = P (1 + 20/100)
⇒ $6660 = P (100 + 20/100)
⇒ $6660 = P × 120/100
⇒ P × 120/100 = $6660
⇒ P = 6660/120/100
⇒ P = 6660 × 100/120
⇒ P = 6660 × 100/120
⇒ P = 666000/120
⇒ P = $5550
Thus, the sum borrowed (P) = $5550 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 6660, then the Principal = 100/120 × 6660
= 100 × 6660/120
= 666000/120
= 5550
Thus, Principal = $5550
Thus, the sum borrowed = $5550 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(3) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
(8) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(10) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.