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) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?
(4) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.
(6) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.
(10) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?