Question:
Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $3922
Rate of Simple Interest (R) = 2%
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
$3922 = P (1 + 2% × 3)
⇒ $3922 = P (1 + 2/100 × 3)
⇒ $3922 = P (1 + 2 × 3/100)
⇒ $3922 = P (1 + 6/100)
⇒ $3922 = P (100 + 6/100)
⇒ $3922 = P × 106/100
⇒ P × 106/100 = $3922
⇒ P = 3922/106/100
⇒ P = 3922 × 100/106
⇒ P = 3922 × 100/106
⇒ P = 392200/106
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 3922, then the Principal = 100/106 × 3922
= 100 × 3922/106
= 392200/106
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.
(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?
(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 5% simple interest?
(8) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.