Question:
If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4900
Solution And Explanation
Solution
Given,
Amount (A) = $5880
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
$5880 = P (1 + 5% × 4)
⇒ $5880 = P (1 + 5/100 × 4)
⇒ $5880 = P (1 + 5 × 4/100)
⇒ $5880 = P (1 + 20/100)
⇒ $5880 = P (100 + 20/100)
⇒ $5880 = P × 120/100
⇒ P × 120/100 = $5880
⇒ P = 5880/120/100
⇒ P = 5880 × 100/120
⇒ P = 5880 × 100/120
⇒ P = 588000/120
⇒ P = $4900
Thus, the sum borrowed (P) = $4900 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 5880, then the Principal = 100/120 × 5880
= 100 × 5880/120
= 588000/120
= 4900
Thus, Principal = $4900
Thus, the sum borrowed = $4900 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.
(3) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(5) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.
(10) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 4 years.