Question:
How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
Correct Answer
$7250
Solution And Explanation
Solution
Given,
Amount (A) = $9062.5
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
$9062.5 = P (1 + 5% × 5)
⇒ $9062.5 = P (1 + 5/100 × 5)
⇒ $9062.5 = P (1 + 5 × 5/100)
⇒ $9062.5 = P (1 + 25/100)
⇒ $9062.5 = P (100 + 25/100)
⇒ $9062.5 = P × 125/100
⇒ P × 125/100 = $9062.5
⇒ P = 9062.5/125/100
⇒ P = 9062.5 × 100/125
⇒ P = 9062.5 × 100/125
⇒ P = 906250/125
⇒ P = $7250
Thus, the sum borrowed (P) = $7250 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 9062.5, then the Principal = 100/125 × 9062.5
= 100 × 9062.5/125
= 906250/125
= 7250
Thus, Principal = $7250
Thus, the sum borrowed = $7250 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(2) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.
(3) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.
(6) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.
(8) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.