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) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?
(3) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.
(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(6) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(7) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(8) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.
(10) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.