Question:
( 1 of 10 ) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(A) 4 47/50 Or, 247/50
(B) 8 47/50 Or, 447/50
(C) 4 141/50 Or, 341/50
(D) 4 94/50 Or, 294/50
You selected
$4496.25
Correct Answer
$5450
Solution And Explanation
Solution
Given,
Amount (A) = $5995
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
$5995 = P (1 + 2% × 5)
⇒ $5995 = P (1 + 2/100 × 5)
⇒ $5995 = P (1 + 2 × 5/100)
⇒ $5995 = P (1 + 10/100)
⇒ $5995 = P (100 + 10/100)
⇒ $5995 = P × 110/100
⇒ P × 110/100 = $5995
⇒ P = 5995/110/100
⇒ P = 5995 × 100/110
⇒ P = 5995 × 100/110
⇒ P = 599500/110
⇒ P = $5450
Thus, the sum borrowed (P) = $5450 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 5995, then the Principal = 100/110 × 5995
= 100 × 5995/110
= 599500/110
= 5450
Thus, Principal = $5450
Thus, the sum borrowed = $5450 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
(3) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(5) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
(8) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
(9) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.