Question:
How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
Correct Answer
$7850
Solution And Explanation
Solution
Given,
Amount (A) = $9812.5
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
$9812.5 = P (1 + 5% × 5)
⇒ $9812.5 = P (1 + 5/100 × 5)
⇒ $9812.5 = P (1 + 5 × 5/100)
⇒ $9812.5 = P (1 + 25/100)
⇒ $9812.5 = P (100 + 25/100)
⇒ $9812.5 = P × 125/100
⇒ P × 125/100 = $9812.5
⇒ P = 9812.5/125/100
⇒ P = 9812.5 × 100/125
⇒ P = 9812.5 × 100/125
⇒ P = 981250/125
⇒ P = $7850
Thus, the sum borrowed (P) = $7850 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 9812.5, then the Principal = 100/125 × 9812.5
= 100 × 9812.5/125
= 981250/125
= 7850
Thus, Principal = $7850
Thus, the sum borrowed = $7850 Answer
Similar Questions
(1) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?
(3) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
(5) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.
(6) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(9) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.