Question:
If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4800
Solution And Explanation
Solution
Given,
Amount (A) = $5184
Rate of Simple Interest (R) = 2%
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
$5184 = P (1 + 2% × 4)
⇒ $5184 = P (1 + 2/100 × 4)
⇒ $5184 = P (1 + 2 × 4/100)
⇒ $5184 = P (1 + 8/100)
⇒ $5184 = P (100 + 8/100)
⇒ $5184 = P × 108/100
⇒ P × 108/100 = $5184
⇒ P = 5184/108/100
⇒ P = 5184 × 100/108
⇒ P = 5184 × 100/108
⇒ P = 518400/108
⇒ P = $4800
Thus, the sum borrowed (P) = $4800 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 5184, then the Principal = 100/108 × 5184
= 100 × 5184/108
= 518400/108
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?
(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 3% simple interest?
(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(6) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.
(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?
(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(9) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?