Question:
( 1 of 10 ) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(A) 753
(B) 376
(C) 751
(D) 752
You selected
$3690
Correct Answer
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4920
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
$4920 = P (1 + 5% × 4)
⇒ $4920 = P (1 + 5/100 × 4)
⇒ $4920 = P (1 + 5 × 4/100)
⇒ $4920 = P (1 + 20/100)
⇒ $4920 = P (100 + 20/100)
⇒ $4920 = P × 120/100
⇒ P × 120/100 = $4920
⇒ P = 4920/120/100
⇒ P = 4920 × 100/120
⇒ P = 4920 × 100/120
⇒ P = 492000/120
⇒ P = $4100
Thus, the sum borrowed (P) = $4100 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 4920, then the Principal = 100/120 × 4920
= 100 × 4920/120
= 492000/120
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(2) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?
(3) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(7) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.