Question:
How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?
Correct Answer
$7350
Solution And Explanation
Solution
Given,
Amount (A) = $8820
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
$8820 = P (1 + 4% × 5)
⇒ $8820 = P (1 + 4/100 × 5)
⇒ $8820 = P (1 + 4 × 5/100)
⇒ $8820 = P (1 + 20/100)
⇒ $8820 = P (100 + 20/100)
⇒ $8820 = P × 120/100
⇒ P × 120/100 = $8820
⇒ P = 8820/120/100
⇒ P = 8820 × 100/120
⇒ P = 8820 × 100/120
⇒ P = 882000/120
⇒ P = $7350
Thus, the sum borrowed (P) = $7350 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 8820, then the Principal = 100/120 × 8820
= 100 × 8820/120
= 882000/120
= 7350
Thus, Principal = $7350
Thus, the sum borrowed = $7350 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?
(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(4) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?
(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 4% simple interest?
(6) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.
(7) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?
(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.
(9) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.