Question:
( 1 of 10 ) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
(A) 753
(B) 376
(C) 751
(D) 752
You selected
$4702.5
Correct Answer
$5700
Solution And Explanation
Solution
Given,
Amount (A) = $6270
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
$6270 = P (1 + 2% × 5)
⇒ $6270 = P (1 + 2/100 × 5)
⇒ $6270 = P (1 + 2 × 5/100)
⇒ $6270 = P (1 + 10/100)
⇒ $6270 = P (100 + 10/100)
⇒ $6270 = P × 110/100
⇒ P × 110/100 = $6270
⇒ P = 6270/110/100
⇒ P = 6270 × 100/110
⇒ P = 6270 × 100/110
⇒ P = 627000/110
⇒ P = $5700
Thus, the sum borrowed (P) = $5700 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 6270, then the Principal = 100/110 × 6270
= 100 × 6270/110
= 627000/110
= 5700
Thus, Principal = $5700
Thus, the sum borrowed = $5700 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
(5) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(7) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.
(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.