Question:
How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
Correct Answer
$7700
Solution And Explanation
Solution
Given,
Amount (A) = $9625
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
$9625 = P (1 + 5% × 5)
⇒ $9625 = P (1 + 5/100 × 5)
⇒ $9625 = P (1 + 5 × 5/100)
⇒ $9625 = P (1 + 25/100)
⇒ $9625 = P (100 + 25/100)
⇒ $9625 = P × 125/100
⇒ P × 125/100 = $9625
⇒ P = 9625/125/100
⇒ P = 9625 × 100/125
⇒ P = 9625 × 100/125
⇒ P = 962500/125
⇒ P = $7700
Thus, the sum borrowed (P) = $7700 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 9625, then the Principal = 100/125 × 9625
= 100 × 9625/125
= 962500/125
= 7700
Thus, Principal = $7700
Thus, the sum borrowed = $7700 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.
(2) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?
(5) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.
(9) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.