Question:
How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
Correct Answer
$5500
Solution And Explanation
Solution
Given,
Amount (A) = $6600
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
$6600 = P (1 + 4% × 5)
⇒ $6600 = P (1 + 4/100 × 5)
⇒ $6600 = P (1 + 4 × 5/100)
⇒ $6600 = P (1 + 20/100)
⇒ $6600 = P (100 + 20/100)
⇒ $6600 = P × 120/100
⇒ P × 120/100 = $6600
⇒ P = 6600/120/100
⇒ P = 6600 × 100/120
⇒ P = 6600 × 100/120
⇒ P = 660000/120
⇒ P = $5500
Thus, the sum borrowed (P) = $5500 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 6600, then the Principal = 100/120 × 6600
= 100 × 6600/120
= 660000/120
= 5500
Thus, Principal = $5500
Thus, the sum borrowed = $5500 Answer
Similar Questions
(1) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?
(2) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(3) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(4) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
(6) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.
(7) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.