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) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.
(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?