Question:
How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?
Correct Answer
$7450
Solution And Explanation
Solution
Given,
Amount (A) = $8195
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
$8195 = P (1 + 2% × 5)
⇒ $8195 = P (1 + 2/100 × 5)
⇒ $8195 = P (1 + 2 × 5/100)
⇒ $8195 = P (1 + 10/100)
⇒ $8195 = P (100 + 10/100)
⇒ $8195 = P × 110/100
⇒ P × 110/100 = $8195
⇒ P = 8195/110/100
⇒ P = 8195 × 100/110
⇒ P = 8195 × 100/110
⇒ P = 819500/110
⇒ P = $7450
Thus, the sum borrowed (P) = $7450 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 8195, then the Principal = 100/110 × 8195
= 100 × 8195/110
= 819500/110
= 7450
Thus, Principal = $7450
Thus, the sum borrowed = $7450 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.
(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(3) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?
(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(6) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 7 years.
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.
(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.