Question:
How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?
Correct Answer
$7550
Solution And Explanation
Solution
Given,
Amount (A) = $8305
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
$8305 = P (1 + 2% × 5)
⇒ $8305 = P (1 + 2/100 × 5)
⇒ $8305 = P (1 + 2 × 5/100)
⇒ $8305 = P (1 + 10/100)
⇒ $8305 = P (100 + 10/100)
⇒ $8305 = P × 110/100
⇒ P × 110/100 = $8305
⇒ P = 8305/110/100
⇒ P = 8305 × 100/110
⇒ P = 8305 × 100/110
⇒ P = 830500/110
⇒ P = $7550
Thus, the sum borrowed (P) = $7550 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 8305, then the Principal = 100/110 × 8305
= 100 × 8305/110
= 830500/110
= 7550
Thus, Principal = $7550
Thus, the sum borrowed = $7550 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?
(3) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(5) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
(6) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.
(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.
(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.