Question:
How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
Correct Answer
$7900
Solution And Explanation
Solution
Given,
Amount (A) = $9875
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
$9875 = P (1 + 5% × 5)
⇒ $9875 = P (1 + 5/100 × 5)
⇒ $9875 = P (1 + 5 × 5/100)
⇒ $9875 = P (1 + 25/100)
⇒ $9875 = P (100 + 25/100)
⇒ $9875 = P × 125/100
⇒ P × 125/100 = $9875
⇒ P = 9875/125/100
⇒ P = 9875 × 100/125
⇒ P = 9875 × 100/125
⇒ P = 987500/125
⇒ P = $7900
Thus, the sum borrowed (P) = $7900 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 9875, then the Principal = 100/125 × 9875
= 100 × 9875/125
= 987500/125
= 7900
Thus, Principal = $7900
Thus, the sum borrowed = $7900 Answer
Similar Questions
(1) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?
(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(5) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(9) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.