Question:
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.
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) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.
(2) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(3) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(5) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(7) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.
(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?