Question:
How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
Correct Answer
$7900
Solution And Explanation
Solution
Given,
Amount (A) = $9875
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
$9875 = P (1 + 5% × 5)
⇒ $9875 = P (1 + 5/100 × 5)
⇒ $9875 = P (1 + 5 × 5/100)
⇒ $9875 = P (1 + 25/100)
⇒ $9875 = P (100 + 25/100)
⇒ $9875 = P × 125/100
⇒ P × 125/100 = $9875
⇒ P = 9875/125/100
⇒ P = 9875 × 100/125
⇒ P = 9875 × 100/125
⇒ P = 987500/125
⇒ P = $7900
Thus, the sum borrowed (P) = $7900 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 9875, then the Principal = 100/125 × 9875
= 100 × 9875/125
= 987500/125
= 7900
Thus, Principal = $7900
Thus, the sum borrowed = $7900 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(2) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?
(6) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?
(7) Jennifer had to pay $3640 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 after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?