Question:
If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3650
Solution And Explanation
Solution
Given,
Amount (A) = $4088
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
$4088 = P (1 + 3% × 4)
⇒ $4088 = P (1 + 3/100 × 4)
⇒ $4088 = P (1 + 3 × 4/100)
⇒ $4088 = P (1 + 12/100)
⇒ $4088 = P (100 + 12/100)
⇒ $4088 = P × 112/100
⇒ P × 112/100 = $4088
⇒ P = 4088/112/100
⇒ P = 4088 × 100/112
⇒ P = 4088 × 100/112
⇒ P = 408800/112
⇒ 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 = 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 4088, then the Principal = 100/112 × 4088
= 100 × 4088/112
= 408800/112
= 3650
Thus, Principal = $3650
Thus, the sum borrowed = $3650 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.
(4) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.
(8) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.
(10) 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.