Question:
If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3050
Solution And Explanation
Solution
Given,
Amount (A) = $3538
Rate of Simple Interest (R) = 4%
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
$3538 = P (1 + 4% × 4)
⇒ $3538 = P (1 + 4/100 × 4)
⇒ $3538 = P (1 + 4 × 4/100)
⇒ $3538 = P (1 + 16/100)
⇒ $3538 = P (100 + 16/100)
⇒ $3538 = P × 116/100
⇒ P × 116/100 = $3538
⇒ P = 3538/116/100
⇒ P = 3538 × 100/116
⇒ P = 3538 × 100/116
⇒ P = 353800/116
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 3538, then the Principal = 100/116 × 3538
= 100 × 3538/116
= 353800/116
= 3050
Thus, Principal = $3050
Thus, the sum borrowed = $3050 Answer
Similar Questions
(1) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(3) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.