Question:
( 1 of 10 ) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$5390.63
Correct Answer
$5750
Solution And Explanation
Solution
Given,
Amount (A) = $7187.5
Rate of Simple Interest (R) = 5%
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
$7187.5 = P (1 + 5% × 5)
⇒ $7187.5 = P (1 + 5/100 × 5)
⇒ $7187.5 = P (1 + 5 × 5/100)
⇒ $7187.5 = P (1 + 25/100)
⇒ $7187.5 = P (100 + 25/100)
⇒ $7187.5 = P × 125/100
⇒ P × 125/100 = $7187.5
⇒ P = 7187.5/125/100
⇒ P = 7187.5 × 100/125
⇒ P = 7187.5 × 100/125
⇒ P = 718750/125
⇒ P = $5750
Thus, the sum borrowed (P) = $5750 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 = 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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 7187.5, then the Principal = 100/125 × 7187.5
= 100 × 7187.5/125
= 718750/125
= 5750
Thus, Principal = $5750
Thus, the sum borrowed = $5750 Answer
Similar Questions
(1) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?
(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 10% simple interest?
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.
(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.
(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.