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) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(3) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.
(5) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(7) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.