Question:
If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3150
Solution And Explanation
Solution
Given,
Amount (A) = $3780
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
$3780 = P (1 + 5% × 4)
⇒ $3780 = P (1 + 5/100 × 4)
⇒ $3780 = P (1 + 5 × 4/100)
⇒ $3780 = P (1 + 20/100)
⇒ $3780 = P (100 + 20/100)
⇒ $3780 = P × 120/100
⇒ P × 120/100 = $3780
⇒ P = 3780/120/100
⇒ P = 3780 × 100/120
⇒ P = 3780 × 100/120
⇒ P = 378000/120
⇒ P = $3150
Thus, the sum borrowed (P) = $3150 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 3780, then the Principal = 100/120 × 3780
= 100 × 3780/120
= 378000/120
= 3150
Thus, Principal = $3150
Thus, the sum borrowed = $3150 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(2) Mary had to pay $3507.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(5) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.
(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(9) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.
(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.