Question:
Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $4312.5
Rate of Simple Interest (R) = 5%
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
$4312.5 = P (1 + 5% × 3)
⇒ $4312.5 = P (1 + 5/100 × 3)
⇒ $4312.5 = P (1 + 5 × 3/100)
⇒ $4312.5 = P (1 + 15/100)
⇒ $4312.5 = P (100 + 15/100)
⇒ $4312.5 = P × 115/100
⇒ P × 115/100 = $4312.5
⇒ P = 4312.5/115/100
⇒ P = 4312.5 × 100/115
⇒ P = 4312.5 × 100/115
⇒ P = 431250/115
⇒ P = $3750
Thus, the sum borrowed (P) = $3750 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 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 4312.5, then the Principal = 100/115 × 4312.5
= 100 × 4312.5/115
= 431250/115
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(4) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?
(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(10) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?