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) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(2) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(3) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(5) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.
(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(9) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.