Question:
How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?
Correct Answer
$6550
Solution And Explanation
Solution
Given,
Amount (A) = $7860
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
$7860 = P (1 + 4% × 5)
⇒ $7860 = P (1 + 4/100 × 5)
⇒ $7860 = P (1 + 4 × 5/100)
⇒ $7860 = P (1 + 20/100)
⇒ $7860 = P (100 + 20/100)
⇒ $7860 = P × 120/100
⇒ P × 120/100 = $7860
⇒ P = 7860/120/100
⇒ P = 7860 × 100/120
⇒ P = 7860 × 100/120
⇒ P = 786000/120
⇒ P = $6550
Thus, the sum borrowed (P) = $6550 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 7860, then the Principal = 100/120 × 7860
= 100 × 7860/120
= 786000/120
= 6550
Thus, Principal = $6550
Thus, the sum borrowed = $6550 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?
(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?
(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 8 years.
(5) 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.
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.
(7) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.