Question:
Daniel had to pay $4469 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
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4469
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
$4469 = P (1 + 3% × 3)
⇒ $4469 = P (1 + 3/100 × 3)
⇒ $4469 = P (1 + 3 × 3/100)
⇒ $4469 = P (1 + 9/100)
⇒ $4469 = P (100 + 9/100)
⇒ $4469 = P × 109/100
⇒ P × 109/100 = $4469
⇒ P = 4469/109/100
⇒ P = 4469 × 100/109
⇒ P = 4469 × 100/109
⇒ P = 446900/109
⇒ P = $4100
Thus, the sum borrowed (P) = $4100 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 4469, then the Principal = 100/109 × 4469
= 100 × 4469/109
= 446900/109
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?
(5) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 4% simple interest?
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?