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) 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.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.
(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?
(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(6) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?
(8) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.