Question:
If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $3920
Rate of Simple Interest (R) = 3%
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
$3920 = P (1 + 3% × 4)
⇒ $3920 = P (1 + 3/100 × 4)
⇒ $3920 = P (1 + 3 × 4/100)
⇒ $3920 = P (1 + 12/100)
⇒ $3920 = P (100 + 12/100)
⇒ $3920 = P × 112/100
⇒ P × 112/100 = $3920
⇒ P = 3920/112/100
⇒ P = 3920 × 100/112
⇒ P = 3920 × 100/112
⇒ P = 392000/112
⇒ P = $3500
Thus, the sum borrowed (P) = $3500 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 3920, then the Principal = 100/112 × 3920
= 100 × 3920/112
= 392000/112
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 Answer
Similar Questions
(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?
(3) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(6) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?
(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(8) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.