Question:
If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3050
Solution And Explanation
Solution
Given,
Amount (A) = $3660
Rate of Simple Interest (R) = 5%
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
$3660 = P (1 + 5% × 4)
⇒ $3660 = P (1 + 5/100 × 4)
⇒ $3660 = P (1 + 5 × 4/100)
⇒ $3660 = P (1 + 20/100)
⇒ $3660 = P (100 + 20/100)
⇒ $3660 = P × 120/100
⇒ P × 120/100 = $3660
⇒ P = 3660/120/100
⇒ P = 3660 × 100/120
⇒ P = 3660 × 100/120
⇒ P = 366000/120
⇒ P = $3050
Thus, the sum borrowed (P) = $3050 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 3660, then the Principal = 100/120 × 3660
= 100 × 3660/120
= 366000/120
= 3050
Thus, Principal = $3050
Thus, the sum borrowed = $3050 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(4) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(5) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(8) If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.