Question:
How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
Correct Answer
$8000
Solution And Explanation
Solution
Given,
Amount (A) = $10000
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
$10000 = P (1 + 5% × 5)
⇒ $10000 = P (1 + 5/100 × 5)
⇒ $10000 = P (1 + 5 × 5/100)
⇒ $10000 = P (1 + 25/100)
⇒ $10000 = P (100 + 25/100)
⇒ $10000 = P × 125/100
⇒ P × 125/100 = $10000
⇒ P = 10000/125/100
⇒ P = 10000 × 100/125
⇒ P = 10000 × 100/125
⇒ P = 1000000/125
⇒ P = $8000
Thus, the sum borrowed (P) = $8000 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 10000, then the Principal = 100/125 × 10000
= 100 × 10000/125
= 1000000/125
= 8000
Thus, Principal = $8000
Thus, the sum borrowed = $8000 Answer
Similar Questions
(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?
(3) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(8) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?