Question:
If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3650
Solution And Explanation
Solution
Given,
Amount (A) = $4380
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
$4380 = P (1 + 5% × 4)
⇒ $4380 = P (1 + 5/100 × 4)
⇒ $4380 = P (1 + 5 × 4/100)
⇒ $4380 = P (1 + 20/100)
⇒ $4380 = P (100 + 20/100)
⇒ $4380 = P × 120/100
⇒ P × 120/100 = $4380
⇒ P = 4380/120/100
⇒ P = 4380 × 100/120
⇒ P = 4380 × 100/120
⇒ P = 438000/120
⇒ P = $3650
Thus, the sum borrowed (P) = $3650 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 4380, then the Principal = 100/120 × 4380
= 100 × 4380/120
= 438000/120
= 3650
Thus, Principal = $3650
Thus, the sum borrowed = $3650 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(3) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.
(8) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 to clear the loan, then find the time period of the loan.
(9) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.