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 David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(3) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(8) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(10) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?