Question:
How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?
Correct Answer
$7650
Solution And Explanation
Solution
Given,
Amount (A) = $9562.5
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
$9562.5 = P (1 + 5% × 5)
⇒ $9562.5 = P (1 + 5/100 × 5)
⇒ $9562.5 = P (1 + 5 × 5/100)
⇒ $9562.5 = P (1 + 25/100)
⇒ $9562.5 = P (100 + 25/100)
⇒ $9562.5 = P × 125/100
⇒ P × 125/100 = $9562.5
⇒ P = 9562.5/125/100
⇒ P = 9562.5 × 100/125
⇒ P = 9562.5 × 100/125
⇒ P = 956250/125
⇒ P = $7650
Thus, the sum borrowed (P) = $7650 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 9562.5, then the Principal = 100/125 × 9562.5
= 100 × 9562.5/125
= 956250/125
= 7650
Thus, Principal = $7650
Thus, the sum borrowed = $7650 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?
(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
(7) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.
(10) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.