Question:
If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3650
Solution And Explanation
Solution
Given,
Amount (A) = $3942
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
$3942 = P (1 + 2% × 4)
⇒ $3942 = P (1 + 2/100 × 4)
⇒ $3942 = P (1 + 2 × 4/100)
⇒ $3942 = P (1 + 8/100)
⇒ $3942 = P (100 + 8/100)
⇒ $3942 = P × 108/100
⇒ P × 108/100 = $3942
⇒ P = 3942/108/100
⇒ P = 3942 × 100/108
⇒ P = 3942 × 100/108
⇒ P = 394200/108
⇒ P = $3650
Thus, the sum borrowed (P) = $3650 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 3942, then the Principal = 100/108 × 3942
= 100 × 3942/108
= 394200/108
= 3650
Thus, Principal = $3650
Thus, the sum borrowed = $3650 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.
(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(3) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?
(6) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
(7) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(9) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.