Question:
How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
Correct Answer
$6750
Solution And Explanation
Solution
Given,
Amount (A) = $7762.5
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
$7762.5 = P (1 + 3% × 5)
⇒ $7762.5 = P (1 + 3/100 × 5)
⇒ $7762.5 = P (1 + 3 × 5/100)
⇒ $7762.5 = P (1 + 15/100)
⇒ $7762.5 = P (100 + 15/100)
⇒ $7762.5 = P × 115/100
⇒ P × 115/100 = $7762.5
⇒ P = 7762.5/115/100
⇒ P = 7762.5 × 100/115
⇒ P = 7762.5 × 100/115
⇒ P = 776250/115
⇒ P = $6750
Thus, the sum borrowed (P) = $6750 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 7762.5, then the Principal = 100/115 × 7762.5
= 100 × 7762.5/115
= 776250/115
= 6750
Thus, Principal = $6750
Thus, the sum borrowed = $6750 Answer
Similar Questions
(1) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
(3) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.
(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?
(10) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.