Question:
How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?
Correct Answer
$6900
Solution And Explanation
Solution
Given,
Amount (A) = $8280
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
$8280 = P (1 + 4% × 5)
⇒ $8280 = P (1 + 4/100 × 5)
⇒ $8280 = P (1 + 4 × 5/100)
⇒ $8280 = P (1 + 20/100)
⇒ $8280 = P (100 + 20/100)
⇒ $8280 = P × 120/100
⇒ P × 120/100 = $8280
⇒ P = 8280/120/100
⇒ P = 8280 × 100/120
⇒ P = 8280 × 100/120
⇒ P = 828000/120
⇒ P = $6900
Thus, the sum borrowed (P) = $6900 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 8280, then the Principal = 100/120 × 8280
= 100 × 8280/120
= 828000/120
= 6900
Thus, Principal = $6900
Thus, the sum borrowed = $6900 Answer
Similar Questions
(1) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
(2) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(4) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(8) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.
(10) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.