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) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.
(6) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(8) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?
(10) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.