Question:
How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?
Correct Answer
$7750
Solution And Explanation
Solution
Given,
Amount (A) = $9300
Rate of Simple Interest (R) = 4%
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
$9300 = P (1 + 4% × 5)
⇒ $9300 = P (1 + 4/100 × 5)
⇒ $9300 = P (1 + 4 × 5/100)
⇒ $9300 = P (1 + 20/100)
⇒ $9300 = P (100 + 20/100)
⇒ $9300 = P × 120/100
⇒ P × 120/100 = $9300
⇒ P = 9300/120/100
⇒ P = 9300 × 100/120
⇒ P = 9300 × 100/120
⇒ P = 930000/120
⇒ P = $7750
Thus, the sum borrowed (P) = $7750 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 9300, then the Principal = 100/120 × 9300
= 100 × 9300/120
= 930000/120
= 7750
Thus, Principal = $7750
Thus, the sum borrowed = $7750 Answer
Similar Questions
(1) 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?
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
(3) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(4) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 2% simple interest?
(8) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.
(9) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.