Question:
How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
Correct Answer
$7250
Solution And Explanation
Solution
Given,
Amount (A) = $9062.5
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
$9062.5 = P (1 + 5% × 5)
⇒ $9062.5 = P (1 + 5/100 × 5)
⇒ $9062.5 = P (1 + 5 × 5/100)
⇒ $9062.5 = P (1 + 25/100)
⇒ $9062.5 = P (100 + 25/100)
⇒ $9062.5 = P × 125/100
⇒ P × 125/100 = $9062.5
⇒ P = 9062.5/125/100
⇒ P = 9062.5 × 100/125
⇒ P = 9062.5 × 100/125
⇒ P = 906250/125
⇒ P = $7250
Thus, the sum borrowed (P) = $7250 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 9062.5, then the Principal = 100/125 × 9062.5
= 100 × 9062.5/125
= 906250/125
= 7250
Thus, Principal = $7250
Thus, the sum borrowed = $7250 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
(2) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?
(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.
(6) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(8) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.
(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?