Question:
If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3550
Solution And Explanation
Solution
Given,
Amount (A) = $4260
Rate of Simple Interest (R) = 5%
Time (T) = 4 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
$4260 = P (1 + 5% × 4)
⇒ $4260 = P (1 + 5/100 × 4)
⇒ $4260 = P (1 + 5 × 4/100)
⇒ $4260 = P (1 + 20/100)
⇒ $4260 = P (100 + 20/100)
⇒ $4260 = P × 120/100
⇒ P × 120/100 = $4260
⇒ P = 4260/120/100
⇒ P = 4260 × 100/120
⇒ P = 4260 × 100/120
⇒ P = 426000/120
⇒ P = $3550
Thus, the sum borrowed (P) = $3550 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
Calculation of the Amount
Since, in the question, time = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 5 = 20
Thus, simple interest for 4 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 4260, then the Principal = 100/120 × 4260
= 100 × 4260/120
= 426000/120
= 3550
Thus, Principal = $3550
Thus, the sum borrowed = $3550 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(2) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?
(4) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.