Question:
( 1 of 10 ) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(A) 4 47/50 Or, 247/50
(B) 8 47/50 Or, 447/50
(C) 4 141/50 Or, 341/50
(D) 4 94/50 Or, 294/50
You selected
$3915
Correct Answer
$4500
Solution And Explanation
Solution
Given,
Amount (A) = $5220
Rate of Simple Interest (R) = 4%
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
$5220 = P (1 + 4% × 4)
⇒ $5220 = P (1 + 4/100 × 4)
⇒ $5220 = P (1 + 4 × 4/100)
⇒ $5220 = P (1 + 16/100)
⇒ $5220 = P (100 + 16/100)
⇒ $5220 = P × 116/100
⇒ P × 116/100 = $5220
⇒ P = 5220/116/100
⇒ P = 5220 × 100/116
⇒ P = 5220 × 100/116
⇒ P = 522000/116
⇒ P = $4500
Thus, the sum borrowed (P) = $4500 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 5220, then the Principal = 100/116 × 5220
= 100 × 5220/116
= 522000/116
= 4500
Thus, Principal = $4500
Thus, the sum borrowed = $4500 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 8% simple interest?
(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?
(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?
(8) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(10) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.