Question:
How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
Correct Answer
$6100
Solution And Explanation
Solution
Given,
Amount (A) = $7625
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
$7625 = P (1 + 5% × 5)
⇒ $7625 = P (1 + 5/100 × 5)
⇒ $7625 = P (1 + 5 × 5/100)
⇒ $7625 = P (1 + 25/100)
⇒ $7625 = P (100 + 25/100)
⇒ $7625 = P × 125/100
⇒ P × 125/100 = $7625
⇒ P = 7625/125/100
⇒ P = 7625 × 100/125
⇒ P = 7625 × 100/125
⇒ P = 762500/125
⇒ P = $6100
Thus, the sum borrowed (P) = $6100 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 7625, then the Principal = 100/125 × 7625
= 100 × 7625/125
= 762500/125
= 6100
Thus, Principal = $6100
Thus, the sum borrowed = $6100 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.
(3) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(5) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(8) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?