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) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.
(2) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(5) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(7) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(9) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(10) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.