Question:
Sandra had to pay $5117.5 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
$4450
Solution And Explanation
Solution
Given,
Amount (A) = $5117.5
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
$5117.5 = P (1 + 5% × 3)
⇒ $5117.5 = P (1 + 5/100 × 3)
⇒ $5117.5 = P (1 + 5 × 3/100)
⇒ $5117.5 = P (1 + 15/100)
⇒ $5117.5 = P (100 + 15/100)
⇒ $5117.5 = P × 115/100
⇒ P × 115/100 = $5117.5
⇒ P = 5117.5/115/100
⇒ P = 5117.5 × 100/115
⇒ P = 5117.5 × 100/115
⇒ P = 511750/115
⇒ P = $4450
Thus, the sum borrowed (P) = $4450 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 5117.5, then the Principal = 100/115 × 5117.5
= 100 × 5117.5/115
= 511750/115
= 4450
Thus, Principal = $4450
Thus, the sum borrowed = $4450 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.
(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
(5) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(6) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(8) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?