Question:
How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
Correct Answer
$6450
Solution And Explanation
Solution
Given,
Amount (A) = $7417.5
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
$7417.5 = P (1 + 3% × 5)
⇒ $7417.5 = P (1 + 3/100 × 5)
⇒ $7417.5 = P (1 + 3 × 5/100)
⇒ $7417.5 = P (1 + 15/100)
⇒ $7417.5 = P (100 + 15/100)
⇒ $7417.5 = P × 115/100
⇒ P × 115/100 = $7417.5
⇒ P = 7417.5/115/100
⇒ P = 7417.5 × 100/115
⇒ P = 7417.5 × 100/115
⇒ P = 741750/115
⇒ P = $6450
Thus, the sum borrowed (P) = $6450 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 7417.5, then the Principal = 100/115 × 7417.5
= 100 × 7417.5/115
= 741750/115
= 6450
Thus, Principal = $6450
Thus, the sum borrowed = $6450 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?
(3) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(4) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(6) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.
(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(10) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?