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) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?
(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(5) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
(6) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?
(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?