Question:
If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5130
Rate of Simple Interest (R) = 2%
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
$5130 = P (1 + 2% × 4)
⇒ $5130 = P (1 + 2/100 × 4)
⇒ $5130 = P (1 + 2 × 4/100)
⇒ $5130 = P (1 + 8/100)
⇒ $5130 = P (100 + 8/100)
⇒ $5130 = P × 108/100
⇒ P × 108/100 = $5130
⇒ P = 5130/108/100
⇒ P = 5130 × 100/108
⇒ P = 5130 × 100/108
⇒ P = 513000/108
⇒ 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 = 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 = 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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 5130, then the Principal = 100/108 × 5130
= 100 × 5130/108
= 513000/108
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.
(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(8) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.