Question:
If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3250
Solution And Explanation
Solution
Given,
Amount (A) = $3900
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
$3900 = P (1 + 5% × 4)
⇒ $3900 = P (1 + 5/100 × 4)
⇒ $3900 = P (1 + 5 × 4/100)
⇒ $3900 = P (1 + 20/100)
⇒ $3900 = P (100 + 20/100)
⇒ $3900 = P × 120/100
⇒ P × 120/100 = $3900
⇒ P = 3900/120/100
⇒ P = 3900 × 100/120
⇒ P = 3900 × 100/120
⇒ P = 390000/120
⇒ P = $3250
Thus, the sum borrowed (P) = $3250 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 3900, then the Principal = 100/120 × 3900
= 100 × 3900/120
= 390000/120
= 3250
Thus, Principal = $3250
Thus, the sum borrowed = $3250 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?