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) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.
(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(4) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(5) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.
(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(8) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?
(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.