Question:
If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4500
Solution And Explanation
Solution
Given,
Amount (A) = $5040
Rate of Simple Interest (R) = 3%
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
$5040 = P (1 + 3% × 4)
⇒ $5040 = P (1 + 3/100 × 4)
⇒ $5040 = P (1 + 3 × 4/100)
⇒ $5040 = P (1 + 12/100)
⇒ $5040 = P (100 + 12/100)
⇒ $5040 = P × 112/100
⇒ P × 112/100 = $5040
⇒ P = 5040/112/100
⇒ P = 5040 × 100/112
⇒ P = 5040 × 100/112
⇒ P = 504000/112
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 5040, then the Principal = 100/112 × 5040
= 100 × 5040/112
= 504000/112
= 4500
Thus, Principal = $4500
Thus, the sum borrowed = $4500 Answer
Similar Questions
(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?
(2) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.
(5) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(6) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
(9) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?