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 Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
(3) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?
(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.
(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 6% simple interest?
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.