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) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.
(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?
(7) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?
(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.