Question:
( 3 of 10 ) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(A) 11 19/46 days or 11.413 days
(B) 22 19/46 days or 22.413 days
(C) 46 days
(D) 23 days
You selected
$5310
Correct Answer
$5900
Solution And Explanation
Solution
Given,
Amount (A) = $7080
Rate of Simple Interest (R) = 4%
Time (T) = 5 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
$7080 = P (1 + 4% × 5)
⇒ $7080 = P (1 + 4/100 × 5)
⇒ $7080 = P (1 + 4 × 5/100)
⇒ $7080 = P (1 + 20/100)
⇒ $7080 = P (100 + 20/100)
⇒ $7080 = P × 120/100
⇒ P × 120/100 = $7080
⇒ P = 7080/120/100
⇒ P = 7080 × 100/120
⇒ P = 7080 × 100/120
⇒ P = 708000/120
⇒ P = $5900
Thus, the sum borrowed (P) = $5900 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 7080, then the Principal = 100/120 × 7080
= 100 × 7080/120
= 708000/120
= 5900
Thus, Principal = $5900
Thus, the sum borrowed = $5900 Answer
Similar Questions
(1) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
(2) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?
(4) How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
(5) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 8 years.
(10) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.