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) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(2) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 4 years.
(5) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.
(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
(8) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(10) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.