Question:
( 1 of 10 ) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(A) 1264
(B) 1265
(C) 1266
(D) 632.5
You selected
$3363.75
Correct Answer
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4485
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
$4485 = P (1 + 5% × 3)
⇒ $4485 = P (1 + 5/100 × 3)
⇒ $4485 = P (1 + 5 × 3/100)
⇒ $4485 = P (1 + 15/100)
⇒ $4485 = P (100 + 15/100)
⇒ $4485 = P × 115/100
⇒ P × 115/100 = $4485
⇒ P = 4485/115/100
⇒ P = 4485 × 100/115
⇒ P = 4485 × 100/115
⇒ P = 448500/115
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 4485, then the Principal = 100/115 × 4485
= 100 × 4485/115
= 448500/115
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
(3) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.
(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(8) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.