Question:
If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4550
Solution And Explanation
Solution
Given,
Amount (A) = $4914
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
$4914 = P (1 + 2% × 4)
⇒ $4914 = P (1 + 2/100 × 4)
⇒ $4914 = P (1 + 2 × 4/100)
⇒ $4914 = P (1 + 8/100)
⇒ $4914 = P (100 + 8/100)
⇒ $4914 = P × 108/100
⇒ P × 108/100 = $4914
⇒ P = 4914/108/100
⇒ P = 4914 × 100/108
⇒ P = 4914 × 100/108
⇒ P = 491400/108
⇒ P = $4550
Thus, the sum borrowed (P) = $4550 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 4914, then the Principal = 100/108 × 4914
= 100 × 4914/108
= 491400/108
= 4550
Thus, Principal = $4550
Thus, the sum borrowed = $4550 Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(2) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(8) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(9) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.