Question:
How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
Correct Answer
$6900
Solution And Explanation
Solution
Given,
Amount (A) = $8625
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
$8625 = P (1 + 5% × 5)
⇒ $8625 = P (1 + 5/100 × 5)
⇒ $8625 = P (1 + 5 × 5/100)
⇒ $8625 = P (1 + 25/100)
⇒ $8625 = P (100 + 25/100)
⇒ $8625 = P × 125/100
⇒ P × 125/100 = $8625
⇒ P = 8625/125/100
⇒ P = 8625 × 100/125
⇒ P = 8625 × 100/125
⇒ P = 862500/125
⇒ P = $6900
Thus, the sum borrowed (P) = $6900 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 8625, then the Principal = 100/125 × 8625
= 100 × 8625/125
= 862500/125
= 6900
Thus, Principal = $6900
Thus, the sum borrowed = $6900 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.
(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.
(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 8 years.
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(10) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.