Question:
Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$4400
Solution And Explanation
Solution
Given,
Amount (A) = $4796
Rate of Simple Interest (R) = 3%
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
$4796 = P (1 + 3% × 3)
⇒ $4796 = P (1 + 3/100 × 3)
⇒ $4796 = P (1 + 3 × 3/100)
⇒ $4796 = P (1 + 9/100)
⇒ $4796 = P (100 + 9/100)
⇒ $4796 = P × 109/100
⇒ P × 109/100 = $4796
⇒ P = 4796/109/100
⇒ P = 4796 × 100/109
⇒ P = 4796 × 100/109
⇒ P = 479600/109
⇒ P = $4400
Thus, the sum borrowed (P) = $4400 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 = 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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 4796, then the Principal = 100/109 × 4796
= 100 × 4796/109
= 479600/109
= 4400
Thus, Principal = $4400
Thus, the sum borrowed = $4400 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 8% simple interest?
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.
(6) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(7) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(8) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(10) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.