Question:
( 1 of 10 ) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$4657.5
Correct Answer
$5400
Solution And Explanation
Solution
Given,
Amount (A) = $6210
Rate of Simple Interest (R) = 3%
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
$6210 = P (1 + 3% × 5)
⇒ $6210 = P (1 + 3/100 × 5)
⇒ $6210 = P (1 + 3 × 5/100)
⇒ $6210 = P (1 + 15/100)
⇒ $6210 = P (100 + 15/100)
⇒ $6210 = P × 115/100
⇒ P × 115/100 = $6210
⇒ P = 6210/115/100
⇒ P = 6210 × 100/115
⇒ P = 6210 × 100/115
⇒ P = 621000/115
⇒ P = $5400
Thus, the sum borrowed (P) = $5400 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6210, then the Principal = 100/115 × 6210
= 100 × 6210/115
= 621000/115
= 5400
Thus, Principal = $5400
Thus, the sum borrowed = $5400 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(3) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.
(6) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(8) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.
(10) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?