Question:
James had to pay $3450 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
$3000
Solution And Explanation
Solution
Given,
Amount (A) = $3450
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
$3450 = P (1 + 5% × 3)
⇒ $3450 = P (1 + 5/100 × 3)
⇒ $3450 = P (1 + 5 × 3/100)
⇒ $3450 = P (1 + 15/100)
⇒ $3450 = P (100 + 15/100)
⇒ $3450 = P × 115/100
⇒ P × 115/100 = $3450
⇒ P = 3450/115/100
⇒ P = 3450 × 100/115
⇒ P = 3450 × 100/115
⇒ P = 345000/115
⇒ P = $3000
Thus, the sum borrowed (P) = $3000 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 3450, then the Principal = 100/115 × 3450
= 100 × 3450/115
= 345000/115
= 3000
Thus, Principal = $3000
Thus, the sum borrowed = $3000 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.
(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?
(4) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(5) Mary had to pay $3324.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.
(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
(8) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.