Question:
( 1 of 10 ) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$7031.25
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Amount (A) = $9375
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
$9375 = P (1 + 5% × 5)
⇒ $9375 = P (1 + 5/100 × 5)
⇒ $9375 = P (1 + 5 × 5/100)
⇒ $9375 = P (1 + 25/100)
⇒ $9375 = P (100 + 25/100)
⇒ $9375 = P × 125/100
⇒ P × 125/100 = $9375
⇒ P = 9375/125/100
⇒ P = 9375 × 100/125
⇒ P = 9375 × 100/125
⇒ P = 937500/125
⇒ P = $7500
Thus, the sum borrowed (P) = $7500 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 9375, then the Principal = 100/125 × 9375
= 100 × 9375/125
= 937500/125
= 7500
Thus, Principal = $7500
Thus, the sum borrowed = $7500 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(4) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(6) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.
(8) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?
(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?