Question : If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer $3300
Solution & Explanation
Solution
Given,
Amount (A) = $3960
Rate of Simple Interest (R) = 5%
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
$3960 = P (1 + 5% × 4)
⇒ $3960 = P (1 + 5/100 × 4)
⇒ $3960 = P (1 + 5 × 4/100)
⇒ $3960 = P (1 + 20/100)
⇒ $3960 = P (100 + 20/100)
⇒ $3960 = P × 120/100
⇒ P × 120/100 = $3960
⇒ P = 3960/120/100
⇒ P = 3960 × 100/120
⇒ P = 3960 × 100/120
⇒ P = 396000/120
⇒ P = $3300
Thus, the sum borrowed (P) = $3300 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 3960, then the Principal = 100/120 × 3960
= 100 × 3960/120
= 396000/120
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.
(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(6) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.