Question:
Joshua had to pay $5341 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
$4900
Solution And Explanation
Solution
Given,
Amount (A) = $5341
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
$5341 = P (1 + 3% × 3)
⇒ $5341 = P (1 + 3/100 × 3)
⇒ $5341 = P (1 + 3 × 3/100)
⇒ $5341 = P (1 + 9/100)
⇒ $5341 = P (100 + 9/100)
⇒ $5341 = P × 109/100
⇒ P × 109/100 = $5341
⇒ P = 5341/109/100
⇒ P = 5341 × 100/109
⇒ P = 5341 × 100/109
⇒ P = 534100/109
⇒ P = $4900
Thus, the sum borrowed (P) = $4900 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 5341, then the Principal = 100/109 × 5341
= 100 × 5341/109
= 534100/109
= 4900
Thus, Principal = $4900
Thus, the sum borrowed = $4900 Answer
Similar Questions
(1) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?
(4) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.
(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(7) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?
(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(10) 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.