Question:
If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4212
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
$4212 = P (1 + 2% × 4)
⇒ $4212 = P (1 + 2/100 × 4)
⇒ $4212 = P (1 + 2 × 4/100)
⇒ $4212 = P (1 + 8/100)
⇒ $4212 = P (100 + 8/100)
⇒ $4212 = P × 108/100
⇒ P × 108/100 = $4212
⇒ P = 4212/108/100
⇒ P = 4212 × 100/108
⇒ P = 4212 × 100/108
⇒ P = 421200/108
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 4212, then the Principal = 100/108 × 4212
= 100 × 4212/108
= 421200/108
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?
(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(7) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.
(8) James had to pay $3270 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(10) If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.