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) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(3) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(4) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(7) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.
(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(10) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.