Question:
If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4250
Solution And Explanation
Solution
Given,
Amount (A) = $4590
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
$4590 = P (1 + 2% × 4)
⇒ $4590 = P (1 + 2/100 × 4)
⇒ $4590 = P (1 + 2 × 4/100)
⇒ $4590 = P (1 + 8/100)
⇒ $4590 = P (100 + 8/100)
⇒ $4590 = P × 108/100
⇒ P × 108/100 = $4590
⇒ P = 4590/108/100
⇒ P = 4590 × 100/108
⇒ P = 4590 × 100/108
⇒ P = 459000/108
⇒ 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 = 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 4590, then the Principal = 100/108 × 4590
= 100 × 4590/108
= 459000/108
= 4250
Thus, Principal = $4250
Thus, the sum borrowed = $4250 Answer
Similar Questions
(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(2) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(3) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(5) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(7) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(9) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.