Question:
How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?
Correct Answer
$6050
Solution And Explanation
Solution
Given,
Amount (A) = $7562.5
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
$7562.5 = P (1 + 5% × 5)
⇒ $7562.5 = P (1 + 5/100 × 5)
⇒ $7562.5 = P (1 + 5 × 5/100)
⇒ $7562.5 = P (1 + 25/100)
⇒ $7562.5 = P (100 + 25/100)
⇒ $7562.5 = P × 125/100
⇒ P × 125/100 = $7562.5
⇒ P = 7562.5/125/100
⇒ P = 7562.5 × 100/125
⇒ P = 7562.5 × 100/125
⇒ P = 756250/125
⇒ P = $6050
Thus, the sum borrowed (P) = $6050 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 7562.5, then the Principal = 100/125 × 7562.5
= 100 × 7562.5/125
= 756250/125
= 6050
Thus, Principal = $6050
Thus, the sum borrowed = $6050 Answer
Similar Questions
(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(2) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.
(3) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(10) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.