Question:
Ashley had to pay $4959.5 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
$4550
Solution And Explanation
Solution
Given,
Amount (A) = $4959.5
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
$4959.5 = P (1 + 3% × 3)
⇒ $4959.5 = P (1 + 3/100 × 3)
⇒ $4959.5 = P (1 + 3 × 3/100)
⇒ $4959.5 = P (1 + 9/100)
⇒ $4959.5 = P (100 + 9/100)
⇒ $4959.5 = P × 109/100
⇒ P × 109/100 = $4959.5
⇒ P = 4959.5/109/100
⇒ P = 4959.5 × 100/109
⇒ P = 4959.5 × 100/109
⇒ P = 495950/109
⇒ 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 = 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 4959.5, then the Principal = 100/109 × 4959.5
= 100 × 4959.5/109
= 495950/109
= 4550
Thus, Principal = $4550
Thus, the sum borrowed = $4550 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(5) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?
(6) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(8) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.