Question:
How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?
Correct Answer
$5750
Solution And Explanation
Solution
Given,
Amount (A) = $7187.5
Rate of Simple Interest (R) = 5%
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
$7187.5 = P (1 + 5% × 5)
⇒ $7187.5 = P (1 + 5/100 × 5)
⇒ $7187.5 = P (1 + 5 × 5/100)
⇒ $7187.5 = P (1 + 25/100)
⇒ $7187.5 = P (100 + 25/100)
⇒ $7187.5 = P × 125/100
⇒ P × 125/100 = $7187.5
⇒ P = 7187.5/125/100
⇒ P = 7187.5 × 100/125
⇒ P = 7187.5 × 100/125
⇒ P = 718750/125
⇒ P = $5750
Thus, the sum borrowed (P) = $5750 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 7187.5, then the Principal = 100/125 × 7187.5
= 100 × 7187.5/125
= 718750/125
= 5750
Thus, Principal = $5750
Thus, the sum borrowed = $5750 Answer
Similar Questions
(1) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?
(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.