Question:
How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Amount (A) = $6435
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
$6435 = P (1 + 2% × 5)
⇒ $6435 = P (1 + 2/100 × 5)
⇒ $6435 = P (1 + 2 × 5/100)
⇒ $6435 = P (1 + 10/100)
⇒ $6435 = P (100 + 10/100)
⇒ $6435 = P × 110/100
⇒ P × 110/100 = $6435
⇒ P = 6435/110/100
⇒ P = 6435 × 100/110
⇒ P = 6435 × 100/110
⇒ P = 643500/110
⇒ P = $5850
Thus, the sum borrowed (P) = $5850 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 6435, then the Principal = 100/110 × 6435
= 100 × 6435/110
= 643500/110
= 5850
Thus, Principal = $5850
Thus, the sum borrowed = $5850 Answer
Similar Questions
(1) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?
(2) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
(4) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(7) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.
(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?
(9) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 5% simple interest?