Question:
If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3000
Solution And Explanation
Solution
Given,
Amount (A) = $3480
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
$3480 = P (1 + 4% × 4)
⇒ $3480 = P (1 + 4/100 × 4)
⇒ $3480 = P (1 + 4 × 4/100)
⇒ $3480 = P (1 + 16/100)
⇒ $3480 = P (100 + 16/100)
⇒ $3480 = P × 116/100
⇒ P × 116/100 = $3480
⇒ P = 3480/116/100
⇒ P = 3480 × 100/116
⇒ P = 3480 × 100/116
⇒ P = 348000/116
⇒ P = $3000
Thus, the sum borrowed (P) = $3000 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 3480, then the Principal = 100/116 × 3480
= 100 × 3480/116
= 348000/116
= 3000
Thus, Principal = $3000
Thus, the sum borrowed = $3000 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) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(3) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.
(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 5% simple interest?
(8) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.
(10) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.