Question:
If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4000
Solution And Explanation
Solution
Given,
Amount (A) = $4480
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
$4480 = P (1 + 3% × 4)
⇒ $4480 = P (1 + 3/100 × 4)
⇒ $4480 = P (1 + 3 × 4/100)
⇒ $4480 = P (1 + 12/100)
⇒ $4480 = P (100 + 12/100)
⇒ $4480 = P × 112/100
⇒ P × 112/100 = $4480
⇒ P = 4480/112/100
⇒ P = 4480 × 100/112
⇒ P = 4480 × 100/112
⇒ P = 448000/112
⇒ P = $4000
Thus, the sum borrowed (P) = $4000 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 4480, then the Principal = 100/112 × 4480
= 100 × 4480/112
= 448000/112
= 4000
Thus, Principal = $4000
Thus, the sum borrowed = $4000 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.
(2) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?
(6) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(9) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(10) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.