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) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?
(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?
(5) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(10) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.