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) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 3 years.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?
(4) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
(5) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(8) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.
(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?