Question:
If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4900
Solution And Explanation
Solution
Given,
Amount (A) = $5292
Rate of Simple Interest (R) = 2%
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
$5292 = P (1 + 2% × 4)
⇒ $5292 = P (1 + 2/100 × 4)
⇒ $5292 = P (1 + 2 × 4/100)
⇒ $5292 = P (1 + 8/100)
⇒ $5292 = P (100 + 8/100)
⇒ $5292 = P × 108/100
⇒ P × 108/100 = $5292
⇒ P = 5292/108/100
⇒ P = 5292 × 100/108
⇒ P = 5292 × 100/108
⇒ P = 529200/108
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 5292, then the Principal = 100/108 × 5292
= 100 × 5292/108
= 529200/108
= 4900
Thus, Principal = $4900
Thus, the sum borrowed = $4900 Answer
Similar Questions
(1) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.
(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?
(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?
(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.