Question:
( 1 of 10 ) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$6813.75
Correct Answer
$7900
Solution And Explanation
Solution
Given,
Amount (A) = $9085
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
$9085 = P (1 + 3% × 5)
⇒ $9085 = P (1 + 3/100 × 5)
⇒ $9085 = P (1 + 3 × 5/100)
⇒ $9085 = P (1 + 15/100)
⇒ $9085 = P (100 + 15/100)
⇒ $9085 = P × 115/100
⇒ P × 115/100 = $9085
⇒ P = 9085/115/100
⇒ P = 9085 × 100/115
⇒ P = 9085 × 100/115
⇒ P = 908500/115
⇒ P = $7900
Thus, the sum borrowed (P) = $7900 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 9085, then the Principal = 100/115 × 9085
= 100 × 9085/115
= 908500/115
= 7900
Thus, Principal = $7900
Thus, the sum borrowed = $7900 Answer
Similar Questions
(1) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?
(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(7) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.
(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?
(10) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.