Question:
If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3550
Solution And Explanation
Solution
Given,
Amount (A) = $4118
Rate of Simple Interest (R) = 4%
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
$4118 = P (1 + 4% × 4)
⇒ $4118 = P (1 + 4/100 × 4)
⇒ $4118 = P (1 + 4 × 4/100)
⇒ $4118 = P (1 + 16/100)
⇒ $4118 = P (100 + 16/100)
⇒ $4118 = P × 116/100
⇒ P × 116/100 = $4118
⇒ P = 4118/116/100
⇒ P = 4118 × 100/116
⇒ P = 4118 × 100/116
⇒ P = 411800/116
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 4118, then the Principal = 100/116 × 4118
= 100 × 4118/116
= 411800/116
= 3550
Thus, Principal = $3550
Thus, the sum borrowed = $3550 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(3) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(5) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.