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) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(2) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% 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) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?
(8) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 3 years.
(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?