Question:
Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4200
Solution And Explanation
Solution
Given,
Amount (A) = $4452
Rate of Simple Interest (R) = 2%
Time (T) = 3 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
$4452 = P (1 + 2% × 3)
⇒ $4452 = P (1 + 2/100 × 3)
⇒ $4452 = P (1 + 2 × 3/100)
⇒ $4452 = P (1 + 6/100)
⇒ $4452 = P (100 + 6/100)
⇒ $4452 = P × 106/100
⇒ P × 106/100 = $4452
⇒ P = 4452/106/100
⇒ P = 4452 × 100/106
⇒ P = 4452 × 100/106
⇒ P = 445200/106
⇒ P = $4200
Thus, the sum borrowed (P) = $4200 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
Calculation of the Amount
Since, in the question, time = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4452, then the Principal = 100/106 × 4452
= 100 × 4452/106
= 445200/106
= 4200
Thus, Principal = $4200
Thus, the sum borrowed = $4200 Answer
Similar Questions
(1) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?
(2) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(3) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(6) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 4% simple interest?
(9) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.