Question:
How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
Correct Answer
$6900
Solution And Explanation
Solution
Given,
Amount (A) = $7590
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
$7590 = P (1 + 2% × 5)
⇒ $7590 = P (1 + 2/100 × 5)
⇒ $7590 = P (1 + 2 × 5/100)
⇒ $7590 = P (1 + 10/100)
⇒ $7590 = P (100 + 10/100)
⇒ $7590 = P × 110/100
⇒ P × 110/100 = $7590
⇒ P = 7590/110/100
⇒ P = 7590 × 100/110
⇒ P = 7590 × 100/110
⇒ P = 759000/110
⇒ P = $6900
Thus, the sum borrowed (P) = $6900 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 7590, then the Principal = 100/110 × 7590
= 100 × 7590/110
= 759000/110
= 6900
Thus, Principal = $6900
Thus, the sum borrowed = $6900 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?
(3) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(7) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.