Question:
How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?
Correct Answer
$5550
Solution And Explanation
Solution
Given,
Amount (A) = $6382.5
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
$6382.5 = P (1 + 3% × 5)
⇒ $6382.5 = P (1 + 3/100 × 5)
⇒ $6382.5 = P (1 + 3 × 5/100)
⇒ $6382.5 = P (1 + 15/100)
⇒ $6382.5 = P (100 + 15/100)
⇒ $6382.5 = P × 115/100
⇒ P × 115/100 = $6382.5
⇒ P = 6382.5/115/100
⇒ P = 6382.5 × 100/115
⇒ P = 6382.5 × 100/115
⇒ P = 638250/115
⇒ P = $5550
Thus, the sum borrowed (P) = $5550 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 6382.5, then the Principal = 100/115 × 6382.5
= 100 × 6382.5/115
= 638250/115
= 5550
Thus, Principal = $5550
Thus, the sum borrowed = $5550 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?
(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(4) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.
(7) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?