Question:
How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?
Correct Answer
$6250
Solution And Explanation
Solution
Given,
Amount (A) = $7500
Rate of Simple Interest (R) = 4%
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
$7500 = P (1 + 4% × 5)
⇒ $7500 = P (1 + 4/100 × 5)
⇒ $7500 = P (1 + 4 × 5/100)
⇒ $7500 = P (1 + 20/100)
⇒ $7500 = P (100 + 20/100)
⇒ $7500 = P × 120/100
⇒ P × 120/100 = $7500
⇒ P = 7500/120/100
⇒ P = 7500 × 100/120
⇒ P = 7500 × 100/120
⇒ P = 750000/120
⇒ P = $6250
Thus, the sum borrowed (P) = $6250 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 7500, then the Principal = 100/120 × 7500
= 100 × 7500/120
= 750000/120
= 6250
Thus, Principal = $6250
Thus, the sum borrowed = $6250 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?
(3) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(10) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.