Question:
( 1 of 10 ) How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$5865
Correct Answer
$6800
Solution And Explanation
Solution
Given,
Amount (A) = $7820
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
$7820 = P (1 + 3% × 5)
⇒ $7820 = P (1 + 3/100 × 5)
⇒ $7820 = P (1 + 3 × 5/100)
⇒ $7820 = P (1 + 15/100)
⇒ $7820 = P (100 + 15/100)
⇒ $7820 = P × 115/100
⇒ P × 115/100 = $7820
⇒ P = 7820/115/100
⇒ P = 7820 × 100/115
⇒ P = 7820 × 100/115
⇒ P = 782000/115
⇒ P = $6800
Thus, the sum borrowed (P) = $6800 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 7820, then the Principal = 100/115 × 7820
= 100 × 7820/115
= 782000/115
= 6800
Thus, Principal = $6800
Thus, the sum borrowed = $6800 Answer
Similar Questions
(1) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?
(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?
(5) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
(8) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?
(10) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.