Question:
How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
Correct Answer
$7600
Solution And Explanation
Solution
Given,
Amount (A) = $9120
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
$9120 = P (1 + 4% × 5)
⇒ $9120 = P (1 + 4/100 × 5)
⇒ $9120 = P (1 + 4 × 5/100)
⇒ $9120 = P (1 + 20/100)
⇒ $9120 = P (100 + 20/100)
⇒ $9120 = P × 120/100
⇒ P × 120/100 = $9120
⇒ P = 9120/120/100
⇒ P = 9120 × 100/120
⇒ P = 9120 × 100/120
⇒ P = 912000/120
⇒ P = $7600
Thus, the sum borrowed (P) = $7600 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 9120, then the Principal = 100/120 × 9120
= 100 × 9120/120
= 912000/120
= 7600
Thus, Principal = $7600
Thus, the sum borrowed = $7600 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(3) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(6) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(7) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?