Question:
How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?
Correct Answer
$6500
Solution And Explanation
Solution
Given,
Amount (A) = $7800
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
$7800 = P (1 + 4% × 5)
⇒ $7800 = P (1 + 4/100 × 5)
⇒ $7800 = P (1 + 4 × 5/100)
⇒ $7800 = P (1 + 20/100)
⇒ $7800 = P (100 + 20/100)
⇒ $7800 = P × 120/100
⇒ P × 120/100 = $7800
⇒ P = 7800/120/100
⇒ P = 7800 × 100/120
⇒ P = 7800 × 100/120
⇒ P = 780000/120
⇒ P = $6500
Thus, the sum borrowed (P) = $6500 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 7800, then the Principal = 100/120 × 7800
= 100 × 7800/120
= 780000/120
= 6500
Thus, Principal = $6500
Thus, the sum borrowed = $6500 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?
(3) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.
(6) 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.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?
(9) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.