Question:
( 1 of 10 ) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$6468.75
Correct Answer
$6900
Solution And Explanation
Solution
Given,
Amount (A) = $8625
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
$8625 = P (1 + 5% × 5)
⇒ $8625 = P (1 + 5/100 × 5)
⇒ $8625 = P (1 + 5 × 5/100)
⇒ $8625 = P (1 + 25/100)
⇒ $8625 = P (100 + 25/100)
⇒ $8625 = P × 125/100
⇒ P × 125/100 = $8625
⇒ P = 8625/125/100
⇒ P = 8625 × 100/125
⇒ P = 8625 × 100/125
⇒ P = 862500/125
⇒ P = $6900
Thus, the sum borrowed (P) = $6900 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 8625, then the Principal = 100/125 × 8625
= 100 × 8625/125
= 862500/125
= 6900
Thus, Principal = $6900
Thus, the sum borrowed = $6900 Answer
Similar Questions
(1) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?
(2) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(3) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.
(4) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?
(6) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(9) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?