Question:
William had to pay $3815 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
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $3815
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
$3815 = P (1 + 3% × 3)
⇒ $3815 = P (1 + 3/100 × 3)
⇒ $3815 = P (1 + 3 × 3/100)
⇒ $3815 = P (1 + 9/100)
⇒ $3815 = P (100 + 9/100)
⇒ $3815 = P × 109/100
⇒ P × 109/100 = $3815
⇒ P = 3815/109/100
⇒ P = 3815 × 100/109
⇒ P = 3815 × 100/109
⇒ P = 381500/109
⇒ P = $3500
Thus, the sum borrowed (P) = $3500 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 3815, then the Principal = 100/109 × 3815
= 100 × 3815/109
= 381500/109
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(2) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?
(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
(8) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
(9) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?