Question:
If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3650
Solution And Explanation
Solution
Given,
Amount (A) = $4380
Rate of Simple Interest (R) = 5%
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
$4380 = P (1 + 5% × 4)
⇒ $4380 = P (1 + 5/100 × 4)
⇒ $4380 = P (1 + 5 × 4/100)
⇒ $4380 = P (1 + 20/100)
⇒ $4380 = P (100 + 20/100)
⇒ $4380 = P × 120/100
⇒ P × 120/100 = $4380
⇒ P = 4380/120/100
⇒ P = 4380 × 100/120
⇒ P = 4380 × 100/120
⇒ P = 438000/120
⇒ 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 4380, then the Principal = 100/120 × 4380
= 100 × 4380/120
= 438000/120
= 3650
Thus, Principal = $3650
Thus, the sum borrowed = $3650 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(2) If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(4) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.
(7) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.