Question:
If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3350
Solution And Explanation
Solution
Given,
Amount (A) = $3752
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
$3752 = P (1 + 3% × 4)
⇒ $3752 = P (1 + 3/100 × 4)
⇒ $3752 = P (1 + 3 × 4/100)
⇒ $3752 = P (1 + 12/100)
⇒ $3752 = P (100 + 12/100)
⇒ $3752 = P × 112/100
⇒ P × 112/100 = $3752
⇒ P = 3752/112/100
⇒ P = 3752 × 100/112
⇒ P = 3752 × 100/112
⇒ P = 375200/112
⇒ P = $3350
Thus, the sum borrowed (P) = $3350 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 3752, then the Principal = 100/112 × 3752
= 100 × 3752/112
= 375200/112
= 3350
Thus, Principal = $3350
Thus, the sum borrowed = $3350 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.
(3) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.
(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(9) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?