Question:
How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?
Correct Answer
$6850
Solution And Explanation
Solution
Given,
Amount (A) = $8562.5
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
$8562.5 = P (1 + 5% × 5)
⇒ $8562.5 = P (1 + 5/100 × 5)
⇒ $8562.5 = P (1 + 5 × 5/100)
⇒ $8562.5 = P (1 + 25/100)
⇒ $8562.5 = P (100 + 25/100)
⇒ $8562.5 = P × 125/100
⇒ P × 125/100 = $8562.5
⇒ P = 8562.5/125/100
⇒ P = 8562.5 × 100/125
⇒ P = 8562.5 × 100/125
⇒ P = 856250/125
⇒ P = $6850
Thus, the sum borrowed (P) = $6850 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 8562.5, then the Principal = 100/125 × 8562.5
= 100 × 8562.5/125
= 856250/125
= 6850
Thus, Principal = $6850
Thus, the sum borrowed = $6850 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(3) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(4) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(5) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?
(7) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(9) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?
(10) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.