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) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(2) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?
(3) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?
(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 4% simple interest?
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(8) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 4 years.
(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.