Question:
If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4466
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
$4466 = P (1 + 4% × 4)
⇒ $4466 = P (1 + 4/100 × 4)
⇒ $4466 = P (1 + 4 × 4/100)
⇒ $4466 = P (1 + 16/100)
⇒ $4466 = P (100 + 16/100)
⇒ $4466 = P × 116/100
⇒ P × 116/100 = $4466
⇒ P = 4466/116/100
⇒ P = 4466 × 100/116
⇒ P = 4466 × 100/116
⇒ P = 446600/116
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 4466, then the Principal = 100/116 × 4466
= 100 × 4466/116
= 446600/116
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(2) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
(3) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.
(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?
(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?