Question:
How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
Correct Answer
$7050
Solution And Explanation
Solution
Given,
Amount (A) = $7755
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
$7755 = P (1 + 2% × 5)
⇒ $7755 = P (1 + 2/100 × 5)
⇒ $7755 = P (1 + 2 × 5/100)
⇒ $7755 = P (1 + 10/100)
⇒ $7755 = P (100 + 10/100)
⇒ $7755 = P × 110/100
⇒ P × 110/100 = $7755
⇒ P = 7755/110/100
⇒ P = 7755 × 100/110
⇒ P = 7755 × 100/110
⇒ P = 775500/110
⇒ P = $7050
Thus, the sum borrowed (P) = $7050 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 7755, then the Principal = 100/110 × 7755
= 100 × 7755/110
= 775500/110
= 7050
Thus, Principal = $7050
Thus, the sum borrowed = $7050 Answer
Similar Questions
(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(2) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.
(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.
(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
(6) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(10) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.