Question:
If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4250
Solution And Explanation
Solution
Given,
Amount (A) = $4760
Rate of Simple Interest (R) = 3%
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
$4760 = P (1 + 3% × 4)
⇒ $4760 = P (1 + 3/100 × 4)
⇒ $4760 = P (1 + 3 × 4/100)
⇒ $4760 = P (1 + 12/100)
⇒ $4760 = P (100 + 12/100)
⇒ $4760 = P × 112/100
⇒ P × 112/100 = $4760
⇒ P = 4760/112/100
⇒ P = 4760 × 100/112
⇒ P = 4760 × 100/112
⇒ P = 476000/112
⇒ P = $4250
Thus, the sum borrowed (P) = $4250 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4760, then the Principal = 100/112 × 4760
= 100 × 4760/112
= 476000/112
= 4250
Thus, Principal = $4250
Thus, the sum borrowed = $4250 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(5) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(10) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.