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) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(2) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.
(7) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?
(10) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.