Question:
Joseph had to pay $4144 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
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $4144
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
$4144 = P (1 + 4% × 3)
⇒ $4144 = P (1 + 4/100 × 3)
⇒ $4144 = P (1 + 4 × 3/100)
⇒ $4144 = P (1 + 12/100)
⇒ $4144 = P (100 + 12/100)
⇒ $4144 = P × 112/100
⇒ P × 112/100 = $4144
⇒ P = 4144/112/100
⇒ P = 4144 × 100/112
⇒ P = 4144 × 100/112
⇒ P = 414400/112
⇒ P = $3700
Thus, the sum borrowed (P) = $3700 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 4144, then the Principal = 100/112 × 4144
= 100 × 4144/112
= 414400/112
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.
(2) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?
(5) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(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) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(9) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?