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) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 4 years.
(3) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(9) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
(10) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?