Question:
How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?
Correct Answer
$5550
Solution And Explanation
Solution
Given,
Amount (A) = $6937.5
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
$6937.5 = P (1 + 5% × 5)
⇒ $6937.5 = P (1 + 5/100 × 5)
⇒ $6937.5 = P (1 + 5 × 5/100)
⇒ $6937.5 = P (1 + 25/100)
⇒ $6937.5 = P (100 + 25/100)
⇒ $6937.5 = P × 125/100
⇒ P × 125/100 = $6937.5
⇒ P = 6937.5/125/100
⇒ P = 6937.5 × 100/125
⇒ P = 6937.5 × 100/125
⇒ P = 693750/125
⇒ P = $5550
Thus, the sum borrowed (P) = $5550 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 6937.5, then the Principal = 100/125 × 6937.5
= 100 × 6937.5/125
= 693750/125
= 5550
Thus, Principal = $5550
Thus, the sum borrowed = $5550 Answer
Similar Questions
(1) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?
(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?
(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?
(6) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?
(10) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.