Question:
If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4500
Solution And Explanation
Solution
Given,
Amount (A) = $4860
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
$4860 = P (1 + 2% × 4)
⇒ $4860 = P (1 + 2/100 × 4)
⇒ $4860 = P (1 + 2 × 4/100)
⇒ $4860 = P (1 + 8/100)
⇒ $4860 = P (100 + 8/100)
⇒ $4860 = P × 108/100
⇒ P × 108/100 = $4860
⇒ P = 4860/108/100
⇒ P = 4860 × 100/108
⇒ P = 4860 × 100/108
⇒ P = 486000/108
⇒ P = $4500
Thus, the sum borrowed (P) = $4500 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 4860, then the Principal = 100/108 × 4860
= 100 × 4860/108
= 486000/108
= 4500
Thus, Principal = $4500
Thus, the sum borrowed = $4500 Answer
Similar Questions
(1) Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?
(3) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(5) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?
(6) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.
(8) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.