Question:
How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?
Correct Answer
$7100
Solution And Explanation
Solution
Given,
Amount (A) = $7810
Rate of Simple Interest (R) = 2%
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
$7810 = P (1 + 2% × 5)
⇒ $7810 = P (1 + 2/100 × 5)
⇒ $7810 = P (1 + 2 × 5/100)
⇒ $7810 = P (1 + 10/100)
⇒ $7810 = P (100 + 10/100)
⇒ $7810 = P × 110/100
⇒ P × 110/100 = $7810
⇒ P = 7810/110/100
⇒ P = 7810 × 100/110
⇒ P = 7810 × 100/110
⇒ P = 781000/110
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7810, then the Principal = 100/110 × 7810
= 100 × 7810/110
= 781000/110
= 7100
Thus, Principal = $7100
Thus, the sum borrowed = $7100 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(2) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(8) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.