Question:
How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Amount (A) = $9375
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
$9375 = P (1 + 5% × 5)
⇒ $9375 = P (1 + 5/100 × 5)
⇒ $9375 = P (1 + 5 × 5/100)
⇒ $9375 = P (1 + 25/100)
⇒ $9375 = P (100 + 25/100)
⇒ $9375 = P × 125/100
⇒ P × 125/100 = $9375
⇒ P = 9375/125/100
⇒ P = 9375 × 100/125
⇒ P = 9375 × 100/125
⇒ P = 937500/125
⇒ P = $7500
Thus, the sum borrowed (P) = $7500 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 9375, then the Principal = 100/125 × 9375
= 100 × 9375/125
= 937500/125
= 7500
Thus, Principal = $7500
Thus, the sum borrowed = $7500 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.
(5) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?
(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?
(9) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(10) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.