Question:
If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3800
Solution And Explanation
Solution
Given,
Amount (A) = $4104
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
$4104 = P (1 + 2% × 4)
⇒ $4104 = P (1 + 2/100 × 4)
⇒ $4104 = P (1 + 2 × 4/100)
⇒ $4104 = P (1 + 8/100)
⇒ $4104 = P (100 + 8/100)
⇒ $4104 = P × 108/100
⇒ P × 108/100 = $4104
⇒ P = 4104/108/100
⇒ P = 4104 × 100/108
⇒ P = 4104 × 100/108
⇒ P = 410400/108
⇒ P = $3800
Thus, the sum borrowed (P) = $3800 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 4104, then the Principal = 100/108 × 4104
= 100 × 4104/108
= 410400/108
= 3800
Thus, Principal = $3800
Thus, the sum borrowed = $3800 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(2) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 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 6% simple interest for 8 years.
(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?
(5) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(6) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.