Question:
If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4850
Solution And Explanation
Solution
Given,
Amount (A) = $5820
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
$5820 = P (1 + 5% × 4)
⇒ $5820 = P (1 + 5/100 × 4)
⇒ $5820 = P (1 + 5 × 4/100)
⇒ $5820 = P (1 + 20/100)
⇒ $5820 = P (100 + 20/100)
⇒ $5820 = P × 120/100
⇒ P × 120/100 = $5820
⇒ P = 5820/120/100
⇒ P = 5820 × 100/120
⇒ P = 5820 × 100/120
⇒ P = 582000/120
⇒ P = $4850
Thus, the sum borrowed (P) = $4850 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 5820, then the Principal = 100/120 × 5820
= 100 × 5820/120
= 582000/120
= 4850
Thus, Principal = $4850
Thus, the sum borrowed = $4850 Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.
(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.
(10) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?