Question:
How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
Correct Answer
$5600
Solution And Explanation
Solution
Given,
Amount (A) = $6720
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
$6720 = P (1 + 4% × 5)
⇒ $6720 = P (1 + 4/100 × 5)
⇒ $6720 = P (1 + 4 × 5/100)
⇒ $6720 = P (1 + 20/100)
⇒ $6720 = P (100 + 20/100)
⇒ $6720 = P × 120/100
⇒ P × 120/100 = $6720
⇒ P = 6720/120/100
⇒ P = 6720 × 100/120
⇒ P = 6720 × 100/120
⇒ P = 672000/120
⇒ P = $5600
Thus, the sum borrowed (P) = $5600 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 6720, then the Principal = 100/120 × 6720
= 100 × 6720/120
= 672000/120
= 5600
Thus, Principal = $5600
Thus, the sum borrowed = $5600 Answer
Similar Questions
(1) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?
(4) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.
(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
(7) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.