Question:
How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $5750
Rate of Simple Interest (R) = 3%
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
$5750 = P (1 + 3% × 5)
⇒ $5750 = P (1 + 3/100 × 5)
⇒ $5750 = P (1 + 3 × 5/100)
⇒ $5750 = P (1 + 15/100)
⇒ $5750 = P (100 + 15/100)
⇒ $5750 = P × 115/100
⇒ P × 115/100 = $5750
⇒ P = 5750/115/100
⇒ P = 5750 × 100/115
⇒ P = 5750 × 100/115
⇒ P = 575000/115
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 5750, then the Principal = 100/115 × 5750
= 100 × 5750/115
= 575000/115
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?
(3) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?
(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.