Question:
How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
Correct Answer
$7950
Solution And Explanation
Solution
Given,
Amount (A) = $9937.5
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
$9937.5 = P (1 + 5% × 5)
⇒ $9937.5 = P (1 + 5/100 × 5)
⇒ $9937.5 = P (1 + 5 × 5/100)
⇒ $9937.5 = P (1 + 25/100)
⇒ $9937.5 = P (100 + 25/100)
⇒ $9937.5 = P × 125/100
⇒ P × 125/100 = $9937.5
⇒ P = 9937.5/125/100
⇒ P = 9937.5 × 100/125
⇒ P = 9937.5 × 100/125
⇒ P = 993750/125
⇒ P = $7950
Thus, the sum borrowed (P) = $7950 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 9937.5, then the Principal = 100/125 × 9937.5
= 100 × 9937.5/125
= 993750/125
= 7950
Thus, Principal = $7950
Thus, the sum borrowed = $7950 Answer
Similar Questions
(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(2) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(5) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(7) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(9) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?