Question:
How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?
Correct Answer
$6150
Solution And Explanation
Solution
Given,
Amount (A) = $7380
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
$7380 = P (1 + 4% × 5)
⇒ $7380 = P (1 + 4/100 × 5)
⇒ $7380 = P (1 + 4 × 5/100)
⇒ $7380 = P (1 + 20/100)
⇒ $7380 = P (100 + 20/100)
⇒ $7380 = P × 120/100
⇒ P × 120/100 = $7380
⇒ P = 7380/120/100
⇒ P = 7380 × 100/120
⇒ P = 7380 × 100/120
⇒ P = 738000/120
⇒ P = $6150
Thus, the sum borrowed (P) = $6150 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 7380, then the Principal = 100/120 × 7380
= 100 × 7380/120
= 738000/120
= 6150
Thus, Principal = $6150
Thus, the sum borrowed = $6150 Answer
Similar Questions
(1) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(4) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.
(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.