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) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(4) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(5) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.
(6) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?
(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(9) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.