Question:
How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
Correct Answer
$6800
Solution And Explanation
Solution
Given,
Amount (A) = $8500
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
$8500 = P (1 + 5% × 5)
⇒ $8500 = P (1 + 5/100 × 5)
⇒ $8500 = P (1 + 5 × 5/100)
⇒ $8500 = P (1 + 25/100)
⇒ $8500 = P (100 + 25/100)
⇒ $8500 = P × 125/100
⇒ P × 125/100 = $8500
⇒ P = 8500/125/100
⇒ P = 8500 × 100/125
⇒ P = 8500 × 100/125
⇒ P = 850000/125
⇒ P = $6800
Thus, the sum borrowed (P) = $6800 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 8500, then the Principal = 100/125 × 8500
= 100 × 8500/125
= 850000/125
= 6800
Thus, Principal = $6800
Thus, the sum borrowed = $6800 Answer
Similar Questions
(1) 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.
(2) 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.
(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(4) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(5) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.
(7) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(8) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(10) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.