Question:
( 1 of 10 ) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$4873.13
Correct Answer
$5650
Solution And Explanation
Solution
Given,
Amount (A) = $6497.5
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
$6497.5 = P (1 + 3% × 5)
⇒ $6497.5 = P (1 + 3/100 × 5)
⇒ $6497.5 = P (1 + 3 × 5/100)
⇒ $6497.5 = P (1 + 15/100)
⇒ $6497.5 = P (100 + 15/100)
⇒ $6497.5 = P × 115/100
⇒ P × 115/100 = $6497.5
⇒ P = 6497.5/115/100
⇒ P = 6497.5 × 100/115
⇒ P = 6497.5 × 100/115
⇒ P = 649750/115
⇒ P = $5650
Thus, the sum borrowed (P) = $5650 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 6497.5, then the Principal = 100/115 × 6497.5
= 100 × 6497.5/115
= 649750/115
= 5650
Thus, Principal = $5650
Thus, the sum borrowed = $5650 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?
(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?
(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(6) 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.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.
(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 5% simple interest?
(9) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.