Question:
( 1 of 10 ) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 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
$4207.5
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Amount (A) = $5610
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
$5610 = P (1 + 2% × 5)
⇒ $5610 = P (1 + 2/100 × 5)
⇒ $5610 = P (1 + 2 × 5/100)
⇒ $5610 = P (1 + 10/100)
⇒ $5610 = P (100 + 10/100)
⇒ $5610 = P × 110/100
⇒ P × 110/100 = $5610
⇒ P = 5610/110/100
⇒ P = 5610 × 100/110
⇒ P = 5610 × 100/110
⇒ P = 561000/110
⇒ P = $5100
Thus, the sum borrowed (P) = $5100 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 5610, then the Principal = 100/110 × 5610
= 100 × 5610/110
= 561000/110
= 5100
Thus, Principal = $5100
Thus, the sum borrowed = $5100 Answer
Similar Questions
(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(5) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(7) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(8) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.