Question:
How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Amount (A) = $7865
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
$7865 = P (1 + 2% × 5)
⇒ $7865 = P (1 + 2/100 × 5)
⇒ $7865 = P (1 + 2 × 5/100)
⇒ $7865 = P (1 + 10/100)
⇒ $7865 = P (100 + 10/100)
⇒ $7865 = P × 110/100
⇒ P × 110/100 = $7865
⇒ P = 7865/110/100
⇒ P = 7865 × 100/110
⇒ P = 7865 × 100/110
⇒ P = 786500/110
⇒ P = $7150
Thus, the sum borrowed (P) = $7150 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 7865, then the Principal = 100/110 × 7865
= 100 × 7865/110
= 786500/110
= 7150
Thus, Principal = $7150
Thus, the sum borrowed = $7150 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.
(3) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.
(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 5% simple interest?
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(8) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(9) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.
(10) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.