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) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(2) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(4) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(5) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?
(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?
(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?
(8) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
(10) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.