Question:
If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4620
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
$4620 = P (1 + 5% × 4)
⇒ $4620 = P (1 + 5/100 × 4)
⇒ $4620 = P (1 + 5 × 4/100)
⇒ $4620 = P (1 + 20/100)
⇒ $4620 = P (100 + 20/100)
⇒ $4620 = P × 120/100
⇒ P × 120/100 = $4620
⇒ P = 4620/120/100
⇒ P = 4620 × 100/120
⇒ P = 4620 × 100/120
⇒ P = 462000/120
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 4620, then the Principal = 100/120 × 4620
= 100 × 4620/120
= 462000/120
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.
(2) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?
(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?
(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.