Question:
How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?
Correct Answer
$7100
Solution And Explanation
Solution
Given,
Amount (A) = $8165
Rate of Simple Interest (R) = 3%
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
$8165 = P (1 + 3% × 5)
⇒ $8165 = P (1 + 3/100 × 5)
⇒ $8165 = P (1 + 3 × 5/100)
⇒ $8165 = P (1 + 15/100)
⇒ $8165 = P (100 + 15/100)
⇒ $8165 = P × 115/100
⇒ P × 115/100 = $8165
⇒ P = 8165/115/100
⇒ P = 8165 × 100/115
⇒ P = 8165 × 100/115
⇒ P = 816500/115
⇒ P = $7100
Thus, the sum borrowed (P) = $7100 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 8165, then the Principal = 100/115 × 8165
= 100 × 8165/115
= 816500/115
= 7100
Thus, Principal = $7100
Thus, the sum borrowed = $7100 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.
(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(7) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.
(9) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(10) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.