Question:
How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
Correct Answer
$5750
Solution And Explanation
Solution
Given,
Amount (A) = $6612.5
Rate of Simple Interest (R) = 3%
Time (T) = 5 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
$6612.5 = P (1 + 3% × 5)
⇒ $6612.5 = P (1 + 3/100 × 5)
⇒ $6612.5 = P (1 + 3 × 5/100)
⇒ $6612.5 = P (1 + 15/100)
⇒ $6612.5 = P (100 + 15/100)
⇒ $6612.5 = P × 115/100
⇒ P × 115/100 = $6612.5
⇒ P = 6612.5/115/100
⇒ P = 6612.5 × 100/115
⇒ P = 6612.5 × 100/115
⇒ P = 661250/115
⇒ P = $5750
Thus, the sum borrowed (P) = $5750 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6612.5, then the Principal = 100/115 × 6612.5
= 100 × 6612.5/115
= 661250/115
= 5750
Thus, Principal = $5750
Thus, the sum borrowed = $5750 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 5% simple interest?
(2) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?
(3) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(5) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(6) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(8) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.