Question:
If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4648
Rate of Simple Interest (R) = 3%
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
$4648 = P (1 + 3% × 4)
⇒ $4648 = P (1 + 3/100 × 4)
⇒ $4648 = P (1 + 3 × 4/100)
⇒ $4648 = P (1 + 12/100)
⇒ $4648 = P (100 + 12/100)
⇒ $4648 = P × 112/100
⇒ P × 112/100 = $4648
⇒ P = 4648/112/100
⇒ P = 4648 × 100/112
⇒ P = 4648 × 100/112
⇒ P = 464800/112
⇒ P = $4150
Thus, the sum borrowed (P) = $4150 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4648, then the Principal = 100/112 × 4648
= 100 × 4648/112
= 464800/112
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.
(4) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?
(9) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?