Question:
If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3550
Solution And Explanation
Solution
Given,
Amount (A) = $3834
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
$3834 = P (1 + 2% × 4)
⇒ $3834 = P (1 + 2/100 × 4)
⇒ $3834 = P (1 + 2 × 4/100)
⇒ $3834 = P (1 + 8/100)
⇒ $3834 = P (100 + 8/100)
⇒ $3834 = P × 108/100
⇒ P × 108/100 = $3834
⇒ P = 3834/108/100
⇒ P = 3834 × 100/108
⇒ P = 3834 × 100/108
⇒ P = 383400/108
⇒ 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 = 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 3834, then the Principal = 100/108 × 3834
= 100 × 3834/108
= 383400/108
= 3550
Thus, Principal = $3550
Thus, the sum borrowed = $3550 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(4) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(7) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
(9) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.