Question:
How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?
Correct Answer
$5800
Solution And Explanation
Solution
Given,
Amount (A) = $6960
Rate of Simple Interest (R) = 4%
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
$6960 = P (1 + 4% × 5)
⇒ $6960 = P (1 + 4/100 × 5)
⇒ $6960 = P (1 + 4 × 5/100)
⇒ $6960 = P (1 + 20/100)
⇒ $6960 = P (100 + 20/100)
⇒ $6960 = P × 120/100
⇒ P × 120/100 = $6960
⇒ P = 6960/120/100
⇒ P = 6960 × 100/120
⇒ P = 6960 × 100/120
⇒ P = 696000/120
⇒ P = $5800
Thus, the sum borrowed (P) = $5800 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 6960, then the Principal = 100/120 × 6960
= 100 × 6960/120
= 696000/120
= 5800
Thus, Principal = $5800
Thus, the sum borrowed = $5800 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(2) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?
(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(5) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?
(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(8) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?