Question:
How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?
Correct Answer
$6250
Solution And Explanation
Solution
Given,
Amount (A) = $7187.5
Rate of Simple Interest (R) = 3%
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
$7187.5 = P (1 + 3% × 5)
⇒ $7187.5 = P (1 + 3/100 × 5)
⇒ $7187.5 = P (1 + 3 × 5/100)
⇒ $7187.5 = P (1 + 15/100)
⇒ $7187.5 = P (100 + 15/100)
⇒ $7187.5 = P × 115/100
⇒ P × 115/100 = $7187.5
⇒ P = 7187.5/115/100
⇒ P = 7187.5 × 100/115
⇒ P = 7187.5 × 100/115
⇒ P = 718750/115
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 7187.5, then the Principal = 100/115 × 7187.5
= 100 × 7187.5/115
= 718750/115
= 6250
Thus, Principal = $6250
Thus, the sum borrowed = $6250 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(2) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(4) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(5) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(7) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.