Question:
How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?
Correct Answer
$6400
Solution And Explanation
Solution
Given,
Amount (A) = $7680
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
$7680 = P (1 + 4% × 5)
⇒ $7680 = P (1 + 4/100 × 5)
⇒ $7680 = P (1 + 4 × 5/100)
⇒ $7680 = P (1 + 20/100)
⇒ $7680 = P (100 + 20/100)
⇒ $7680 = P × 120/100
⇒ P × 120/100 = $7680
⇒ P = 7680/120/100
⇒ P = 7680 × 100/120
⇒ P = 7680 × 100/120
⇒ P = 768000/120
⇒ P = $6400
Thus, the sum borrowed (P) = $6400 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 7680, then the Principal = 100/120 × 7680
= 100 × 7680/120
= 768000/120
= 6400
Thus, Principal = $6400
Thus, the sum borrowed = $6400 Answer
Similar Questions
(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?
(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(4) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(6) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.
(8) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.
(9) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.
(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.