Question:
If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3400
Solution And Explanation
Solution
Given,
Amount (A) = $3672
Rate of Simple Interest (R) = 2%
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
$3672 = P (1 + 2% × 4)
⇒ $3672 = P (1 + 2/100 × 4)
⇒ $3672 = P (1 + 2 × 4/100)
⇒ $3672 = P (1 + 8/100)
⇒ $3672 = P (100 + 8/100)
⇒ $3672 = P × 108/100
⇒ P × 108/100 = $3672
⇒ P = 3672/108/100
⇒ P = 3672 × 100/108
⇒ P = 3672 × 100/108
⇒ P = 367200/108
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 3672, then the Principal = 100/108 × 3672
= 100 × 3672/108
= 367200/108
= 3400
Thus, Principal = $3400
Thus, the sum borrowed = $3400 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(2) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.
(4) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.
(6) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(8) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(9) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?