Question:
If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3400
Solution And Explanation
Solution
Given,
Amount (A) = $3808
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
$3808 = P (1 + 3% × 4)
⇒ $3808 = P (1 + 3/100 × 4)
⇒ $3808 = P (1 + 3 × 4/100)
⇒ $3808 = P (1 + 12/100)
⇒ $3808 = P (100 + 12/100)
⇒ $3808 = P × 112/100
⇒ P × 112/100 = $3808
⇒ P = 3808/112/100
⇒ P = 3808 × 100/112
⇒ P = 3808 × 100/112
⇒ P = 380800/112
⇒ P = $3400
Thus, the sum borrowed (P) = $3400 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 3808, then the Principal = 100/112 × 3808
= 100 × 3808/112
= 380800/112
= 3400
Thus, Principal = $3400
Thus, the sum borrowed = $3400 Answer
Similar Questions
(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(2) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(4) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(5) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?
(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?