Question:
How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
Correct Answer
$5750
Solution And Explanation
Solution
Given,
Amount (A) = $6900
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
$6900 = P (1 + 4% × 5)
⇒ $6900 = P (1 + 4/100 × 5)
⇒ $6900 = P (1 + 4 × 5/100)
⇒ $6900 = P (1 + 20/100)
⇒ $6900 = P (100 + 20/100)
⇒ $6900 = P × 120/100
⇒ P × 120/100 = $6900
⇒ P = 6900/120/100
⇒ P = 6900 × 100/120
⇒ P = 6900 × 100/120
⇒ P = 690000/120
⇒ P = $5750
Thus, the sum borrowed (P) = $5750 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 6900, then the Principal = 100/120 × 6900
= 100 × 6900/120
= 690000/120
= 5750
Thus, Principal = $5750
Thus, the sum borrowed = $5750 Answer
Similar Questions
(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(3) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(7) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(9) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.