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) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?
(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?
(5) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(6) Sarah took a loan of $5700 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) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?
(9) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.