Question:
Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $5450
Rate of Simple Interest (R) = 3%
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
$5450 = P (1 + 3% × 3)
⇒ $5450 = P (1 + 3/100 × 3)
⇒ $5450 = P (1 + 3 × 3/100)
⇒ $5450 = P (1 + 9/100)
⇒ $5450 = P (100 + 9/100)
⇒ $5450 = P × 109/100
⇒ P × 109/100 = $5450
⇒ P = 5450/109/100
⇒ P = 5450 × 100/109
⇒ P = 5450 × 100/109
⇒ P = 545000/109
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 = 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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 5450, then the Principal = 100/109 × 5450
= 100 × 5450/109
= 545000/109
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.
(2) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?
(6) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.
(10) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?