Question:
Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$4500
Solution And Explanation
Solution
Given,
Amount (A) = $5040
Rate of Simple Interest (R) = 4%
Time (T) = 3 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 + 4% × 3)
⇒ $5040 = P (1 + 4/100 × 3)
⇒ $5040 = P (1 + 4 × 3/100)
⇒ $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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
Calculation of the Amount
Since, in the question, time = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 4 = 12
Thus, simple interest for 3 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) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(2) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(4) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
(5) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.
(7) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 4 years.