Question:
How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
Correct Answer
$6050
Solution And Explanation
Solution
Given,
Amount (A) = $7260
Rate of Simple Interest (R) = 4%
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
$7260 = P (1 + 4% × 5)
⇒ $7260 = P (1 + 4/100 × 5)
⇒ $7260 = P (1 + 4 × 5/100)
⇒ $7260 = P (1 + 20/100)
⇒ $7260 = P (100 + 20/100)
⇒ $7260 = P × 120/100
⇒ P × 120/100 = $7260
⇒ P = 7260/120/100
⇒ P = 7260 × 100/120
⇒ P = 7260 × 100/120
⇒ P = 726000/120
⇒ P = $6050
Thus, the sum borrowed (P) = $6050 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 7260, then the Principal = 100/120 × 7260
= 100 × 7260/120
= 726000/120
= 6050
Thus, Principal = $6050
Thus, the sum borrowed = $6050 Answer
Similar Questions
(1) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(2) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
(3) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(7) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.