Question:
How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?
Correct Answer
$7400
Solution And Explanation
Solution
Given,
Amount (A) = $8880
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
$8880 = P (1 + 4% × 5)
⇒ $8880 = P (1 + 4/100 × 5)
⇒ $8880 = P (1 + 4 × 5/100)
⇒ $8880 = P (1 + 20/100)
⇒ $8880 = P (100 + 20/100)
⇒ $8880 = P × 120/100
⇒ P × 120/100 = $8880
⇒ P = 8880/120/100
⇒ P = 8880 × 100/120
⇒ P = 8880 × 100/120
⇒ P = 888000/120
⇒ P = $7400
Thus, the sum borrowed (P) = $7400 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 8880, then the Principal = 100/120 × 8880
= 100 × 8880/120
= 888000/120
= 7400
Thus, Principal = $7400
Thus, the sum borrowed = $7400 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(2) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.
(3) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(4) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.
(6) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?
(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.