Question:
How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?
Correct Answer
$6500
Solution And Explanation
Solution
Given,
Amount (A) = $7475
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
$7475 = P (1 + 3% × 5)
⇒ $7475 = P (1 + 3/100 × 5)
⇒ $7475 = P (1 + 3 × 5/100)
⇒ $7475 = P (1 + 15/100)
⇒ $7475 = P (100 + 15/100)
⇒ $7475 = P × 115/100
⇒ P × 115/100 = $7475
⇒ P = 7475/115/100
⇒ P = 7475 × 100/115
⇒ P = 7475 × 100/115
⇒ P = 747500/115
⇒ P = $6500
Thus, the sum borrowed (P) = $6500 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 7475, then the Principal = 100/115 × 7475
= 100 × 7475/115
= 747500/115
= 6500
Thus, Principal = $6500
Thus, the sum borrowed = $6500 Answer
Similar Questions
(1) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(3) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.
(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.
(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?
(8) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.
(9) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(10) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?