Question:
If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3050
Solution And Explanation
Solution
Given,
Amount (A) = $3294
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
$3294 = P (1 + 2% × 4)
⇒ $3294 = P (1 + 2/100 × 4)
⇒ $3294 = P (1 + 2 × 4/100)
⇒ $3294 = P (1 + 8/100)
⇒ $3294 = P (100 + 8/100)
⇒ $3294 = P × 108/100
⇒ P × 108/100 = $3294
⇒ P = 3294/108/100
⇒ P = 3294 × 100/108
⇒ P = 3294 × 100/108
⇒ P = 329400/108
⇒ P = $3050
Thus, the sum borrowed (P) = $3050 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 3294, then the Principal = 100/108 × 3294
= 100 × 3294/108
= 329400/108
= 3050
Thus, Principal = $3050
Thus, the sum borrowed = $3050 Answer
Similar Questions
(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.
(3) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(5) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?
(6) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(7) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.