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 William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?
(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?
(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.
(5) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(6) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.