Question:
( 2 of 10 ) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(A) 258.39 km
(B) 215.33 km
(C) 172.26 km
(D) 137.81 km
You selected
$4248.75
Correct Answer
$5150
Solution And Explanation
Solution
Given,
Amount (A) = $5665
Rate of Simple Interest (R) = 2%
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
$5665 = P (1 + 2% × 5)
⇒ $5665 = P (1 + 2/100 × 5)
⇒ $5665 = P (1 + 2 × 5/100)
⇒ $5665 = P (1 + 10/100)
⇒ $5665 = P (100 + 10/100)
⇒ $5665 = P × 110/100
⇒ P × 110/100 = $5665
⇒ P = 5665/110/100
⇒ P = 5665 × 100/110
⇒ P = 5665 × 100/110
⇒ P = 566500/110
⇒ P = $5150
Thus, the sum borrowed (P) = $5150 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5665, then the Principal = 100/110 × 5665
= 100 × 5665/110
= 566500/110
= 5150
Thus, Principal = $5150
Thus, the sum borrowed = $5150 Answer
Similar Questions
(1) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(3) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(5) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
(6) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?
(7) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.
(10) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?