Question:
If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4980
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
$4980 = P (1 + 5% × 4)
⇒ $4980 = P (1 + 5/100 × 4)
⇒ $4980 = P (1 + 5 × 4/100)
⇒ $4980 = P (1 + 20/100)
⇒ $4980 = P (100 + 20/100)
⇒ $4980 = P × 120/100
⇒ P × 120/100 = $4980
⇒ P = 4980/120/100
⇒ P = 4980 × 100/120
⇒ P = 4980 × 100/120
⇒ P = 498000/120
⇒ P = $4150
Thus, the sum borrowed (P) = $4150 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 4980, then the Principal = 100/120 × 4980
= 100 × 4980/120
= 498000/120
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.
(4) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?
(8) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.