Question:
How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?
Correct Answer
$6000
Solution And Explanation
Solution
Given,
Amount (A) = $6600
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
$6600 = P (1 + 2% × 5)
⇒ $6600 = P (1 + 2/100 × 5)
⇒ $6600 = P (1 + 2 × 5/100)
⇒ $6600 = P (1 + 10/100)
⇒ $6600 = P (100 + 10/100)
⇒ $6600 = P × 110/100
⇒ P × 110/100 = $6600
⇒ P = 6600/110/100
⇒ P = 6600 × 100/110
⇒ P = 6600 × 100/110
⇒ P = 660000/110
⇒ P = $6000
Thus, the sum borrowed (P) = $6000 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 6600, then the Principal = 100/110 × 6600
= 100 × 6600/110
= 660000/110
= 6000
Thus, Principal = $6000
Thus, the sum borrowed = $6000 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(6) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(8) If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?
(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.