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) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(2) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?
(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(4) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(7) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.