Question:
Jennifer had to pay $3737.5 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
$3250
Solution And Explanation
Solution
Given,
Amount (A) = $3737.5
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
$3737.5 = P (1 + 5% × 3)
⇒ $3737.5 = P (1 + 5/100 × 3)
⇒ $3737.5 = P (1 + 5 × 3/100)
⇒ $3737.5 = P (1 + 15/100)
⇒ $3737.5 = P (100 + 15/100)
⇒ $3737.5 = P × 115/100
⇒ P × 115/100 = $3737.5
⇒ P = 3737.5/115/100
⇒ P = 3737.5 × 100/115
⇒ P = 3737.5 × 100/115
⇒ P = 373750/115
⇒ P = $3250
Thus, the sum borrowed (P) = $3250 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 3737.5, then the Principal = 100/115 × 3737.5
= 100 × 3737.5/115
= 373750/115
= 3250
Thus, Principal = $3250
Thus, the sum borrowed = $3250 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?
(4) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(6) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(8) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.
(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?