Question:
How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
Correct Answer
$6700
Solution And Explanation
Solution
Given,
Amount (A) = $7705
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
$7705 = P (1 + 3% × 5)
⇒ $7705 = P (1 + 3/100 × 5)
⇒ $7705 = P (1 + 3 × 5/100)
⇒ $7705 = P (1 + 15/100)
⇒ $7705 = P (100 + 15/100)
⇒ $7705 = P × 115/100
⇒ P × 115/100 = $7705
⇒ P = 7705/115/100
⇒ P = 7705 × 100/115
⇒ P = 7705 × 100/115
⇒ P = 770500/115
⇒ P = $6700
Thus, the sum borrowed (P) = $6700 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 7705, then the Principal = 100/115 × 7705
= 100 × 7705/115
= 770500/115
= 6700
Thus, Principal = $6700
Thus, the sum borrowed = $6700 Answer
Similar Questions
(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?
(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?
(4) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6724 to clear the loan, then find the time period of the loan.
(5) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.
(9) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.