Question:
If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4950
Solution And Explanation
Solution
Given,
Amount (A) = $5940
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
$5940 = P (1 + 5% × 4)
⇒ $5940 = P (1 + 5/100 × 4)
⇒ $5940 = P (1 + 5 × 4/100)
⇒ $5940 = P (1 + 20/100)
⇒ $5940 = P (100 + 20/100)
⇒ $5940 = P × 120/100
⇒ P × 120/100 = $5940
⇒ P = 5940/120/100
⇒ P = 5940 × 100/120
⇒ P = 5940 × 100/120
⇒ P = 594000/120
⇒ P = $4950
Thus, the sum borrowed (P) = $4950 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 5940, then the Principal = 100/120 × 5940
= 100 × 5940/120
= 594000/120
= 4950
Thus, Principal = $4950
Thus, the sum borrowed = $4950 Answer
Similar Questions
(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 3 years.
(2) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.
(6) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 3 years.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?