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 Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?
(2) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(4) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(8) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 10% simple interest?