Question:
Ashley had to pay $5096 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
$4550
Solution And Explanation
Solution
Given,
Amount (A) = $5096
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
$5096 = P (1 + 4% × 3)
⇒ $5096 = P (1 + 4/100 × 3)
⇒ $5096 = P (1 + 4 × 3/100)
⇒ $5096 = P (1 + 12/100)
⇒ $5096 = P (100 + 12/100)
⇒ $5096 = P × 112/100
⇒ P × 112/100 = $5096
⇒ P = 5096/112/100
⇒ P = 5096 × 100/112
⇒ P = 5096 × 100/112
⇒ P = 509600/112
⇒ P = $4550
Thus, the sum borrowed (P) = $4550 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 5096, then the Principal = 100/112 × 5096
= 100 × 5096/112
= 509600/112
= 4550
Thus, Principal = $4550
Thus, the sum borrowed = $4550 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(5) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
(8) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
(9) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.