Question:
Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5462.5
Rate of Simple Interest (R) = 5%
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
$5462.5 = P (1 + 5% × 3)
⇒ $5462.5 = P (1 + 5/100 × 3)
⇒ $5462.5 = P (1 + 5 × 3/100)
⇒ $5462.5 = P (1 + 15/100)
⇒ $5462.5 = P (100 + 15/100)
⇒ $5462.5 = P × 115/100
⇒ P × 115/100 = $5462.5
⇒ P = 5462.5/115/100
⇒ P = 5462.5 × 100/115
⇒ P = 5462.5 × 100/115
⇒ P = 546250/115
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 5462.5, then the Principal = 100/115 × 5462.5
= 100 × 5462.5/115
= 546250/115
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(3) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(4) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?
(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.