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) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(2) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.
(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(5) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.
(9) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?