Question:
If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4250
Solution And Explanation
Solution
Given,
Amount (A) = $5100
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
$5100 = P (1 + 5% × 4)
⇒ $5100 = P (1 + 5/100 × 4)
⇒ $5100 = P (1 + 5 × 4/100)
⇒ $5100 = P (1 + 20/100)
⇒ $5100 = P (100 + 20/100)
⇒ $5100 = P × 120/100
⇒ P × 120/100 = $5100
⇒ P = 5100/120/100
⇒ P = 5100 × 100/120
⇒ P = 5100 × 100/120
⇒ P = 510000/120
⇒ P = $4250
Thus, the sum borrowed (P) = $4250 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 5100, then the Principal = 100/120 × 5100
= 100 × 5100/120
= 510000/120
= 4250
Thus, Principal = $4250
Thus, the sum borrowed = $4250 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
(4) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(9) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?