Question:
How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
Correct Answer
$6350
Solution And Explanation
Solution
Given,
Amount (A) = $6985
Rate of Simple Interest (R) = 2%
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
$6985 = P (1 + 2% × 5)
⇒ $6985 = P (1 + 2/100 × 5)
⇒ $6985 = P (1 + 2 × 5/100)
⇒ $6985 = P (1 + 10/100)
⇒ $6985 = P (100 + 10/100)
⇒ $6985 = P × 110/100
⇒ P × 110/100 = $6985
⇒ P = 6985/110/100
⇒ P = 6985 × 100/110
⇒ P = 6985 × 100/110
⇒ P = 698500/110
⇒ P = $6350
Thus, the sum borrowed (P) = $6350 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 6985, then the Principal = 100/110 × 6985
= 100 × 6985/110
= 698500/110
= 6350
Thus, Principal = $6350
Thus, the sum borrowed = $6350 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(4) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(7) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(8) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(9) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.