Question:
Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $5264
Rate of Simple Interest (R) = 4%
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
$5264 = P (1 + 4% × 3)
⇒ $5264 = P (1 + 4/100 × 3)
⇒ $5264 = P (1 + 4 × 3/100)
⇒ $5264 = P (1 + 12/100)
⇒ $5264 = P (100 + 12/100)
⇒ $5264 = P × 112/100
⇒ P × 112/100 = $5264
⇒ P = 5264/112/100
⇒ P = 5264 × 100/112
⇒ P = 5264 × 100/112
⇒ P = 526400/112
⇒ P = $4700
Thus, the sum borrowed (P) = $4700 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 12
Thus, simple interest for 3 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 5264, then the Principal = 100/112 × 5264
= 100 × 5264/112
= 526400/112
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?
(4) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(10) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.