Question:
How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
Correct Answer
$6250
Solution And Explanation
Solution
Given,
Amount (A) = $6875
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
$6875 = P (1 + 2% × 5)
⇒ $6875 = P (1 + 2/100 × 5)
⇒ $6875 = P (1 + 2 × 5/100)
⇒ $6875 = P (1 + 10/100)
⇒ $6875 = P (100 + 10/100)
⇒ $6875 = P × 110/100
⇒ P × 110/100 = $6875
⇒ P = 6875/110/100
⇒ P = 6875 × 100/110
⇒ P = 6875 × 100/110
⇒ P = 687500/110
⇒ P = $6250
Thus, the sum borrowed (P) = $6250 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 6875, then the Principal = 100/110 × 6875
= 100 × 6875/110
= 687500/110
= 6250
Thus, Principal = $6250
Thus, the sum borrowed = $6250 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.
(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(9) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(10) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.