Question:
How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?
Correct Answer
$6250
Solution And Explanation
Solution
Given,
Amount (A) = $7812.5
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
$7812.5 = P (1 + 5% × 5)
⇒ $7812.5 = P (1 + 5/100 × 5)
⇒ $7812.5 = P (1 + 5 × 5/100)
⇒ $7812.5 = P (1 + 25/100)
⇒ $7812.5 = P (100 + 25/100)
⇒ $7812.5 = P × 125/100
⇒ P × 125/100 = $7812.5
⇒ P = 7812.5/125/100
⇒ P = 7812.5 × 100/125
⇒ P = 7812.5 × 100/125
⇒ P = 781250/125
⇒ 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 = 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 7812.5, then the Principal = 100/125 × 7812.5
= 100 × 7812.5/125
= 781250/125
= 6250
Thus, Principal = $6250
Thus, the sum borrowed = $6250 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(2) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.
(4) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(6) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(7) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(8) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(9) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.