Question:
If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4482
Rate of Simple Interest (R) = 2%
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
$4482 = P (1 + 2% × 4)
⇒ $4482 = P (1 + 2/100 × 4)
⇒ $4482 = P (1 + 2 × 4/100)
⇒ $4482 = P (1 + 8/100)
⇒ $4482 = P (100 + 8/100)
⇒ $4482 = P × 108/100
⇒ P × 108/100 = $4482
⇒ P = 4482/108/100
⇒ P = 4482 × 100/108
⇒ P = 4482 × 100/108
⇒ P = 448200/108
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 4482, then the Principal = 100/108 × 4482
= 100 × 4482/108
= 448200/108
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.
(3) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(4) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.
(6) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?
(7) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(8) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(9) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.