Question:
If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3650
Solution And Explanation
Solution
Given,
Amount (A) = $4234
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
$4234 = P (1 + 4% × 4)
⇒ $4234 = P (1 + 4/100 × 4)
⇒ $4234 = P (1 + 4 × 4/100)
⇒ $4234 = P (1 + 16/100)
⇒ $4234 = P (100 + 16/100)
⇒ $4234 = P × 116/100
⇒ P × 116/100 = $4234
⇒ P = 4234/116/100
⇒ P = 4234 × 100/116
⇒ P = 4234 × 100/116
⇒ P = 423400/116
⇒ P = $3650
Thus, the sum borrowed (P) = $3650 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 4234, then the Principal = 100/116 × 4234
= 100 × 4234/116
= 423400/116
= 3650
Thus, Principal = $3650
Thus, the sum borrowed = $3650 Answer
Similar Questions
(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?
(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?
(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.
(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 7 years.