Question:
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.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5320
Rate of Simple Interest (R) = 3%
Time (T) = 4 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
$5320 = P (1 + 3% × 4)
⇒ $5320 = P (1 + 3/100 × 4)
⇒ $5320 = P (1 + 3 × 4/100)
⇒ $5320 = P (1 + 12/100)
⇒ $5320 = P (100 + 12/100)
⇒ $5320 = P × 112/100
⇒ P × 112/100 = $5320
⇒ P = 5320/112/100
⇒ P = 5320 × 100/112
⇒ P = 5320 × 100/112
⇒ P = 532000/112
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
Calculation of the Amount
Since, in the question, time = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 5320, then the Principal = 100/112 × 5320
= 100 × 5320/112
= 532000/112
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(2) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 8 years.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(5) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(9) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(10) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.