Question:
How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?
Correct Answer
$7350
Solution And Explanation
Solution
Given,
Amount (A) = $9187.5
Rate of Simple Interest (R) = 5%
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
$9187.5 = P (1 + 5% × 5)
⇒ $9187.5 = P (1 + 5/100 × 5)
⇒ $9187.5 = P (1 + 5 × 5/100)
⇒ $9187.5 = P (1 + 25/100)
⇒ $9187.5 = P (100 + 25/100)
⇒ $9187.5 = P × 125/100
⇒ P × 125/100 = $9187.5
⇒ P = 9187.5/125/100
⇒ P = 9187.5 × 100/125
⇒ P = 9187.5 × 100/125
⇒ P = 918750/125
⇒ P = $7350
Thus, the sum borrowed (P) = $7350 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 9187.5, then the Principal = 100/125 × 9187.5
= 100 × 9187.5/125
= 918750/125
= 7350
Thus, Principal = $7350
Thus, the sum borrowed = $7350 Answer
Similar Questions
(1) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?
(4) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
(6) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(7) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.