Question:
If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4158
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
$4158 = P (1 + 2% × 4)
⇒ $4158 = P (1 + 2/100 × 4)
⇒ $4158 = P (1 + 2 × 4/100)
⇒ $4158 = P (1 + 8/100)
⇒ $4158 = P (100 + 8/100)
⇒ $4158 = P × 108/100
⇒ P × 108/100 = $4158
⇒ P = 4158/108/100
⇒ P = 4158 × 100/108
⇒ P = 4158 × 100/108
⇒ P = 415800/108
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 4158, then the Principal = 100/108 × 4158
= 100 × 4158/108
= 415800/108
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(3) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(4) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(5) 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.
(6) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(7) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(9) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.