Question:
How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?
Correct Answer
$5650
Solution And Explanation
Solution
Given,
Amount (A) = $6780
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
$6780 = P (1 + 4% × 5)
⇒ $6780 = P (1 + 4/100 × 5)
⇒ $6780 = P (1 + 4 × 5/100)
⇒ $6780 = P (1 + 20/100)
⇒ $6780 = P (100 + 20/100)
⇒ $6780 = P × 120/100
⇒ P × 120/100 = $6780
⇒ P = 6780/120/100
⇒ P = 6780 × 100/120
⇒ P = 6780 × 100/120
⇒ P = 678000/120
⇒ P = $5650
Thus, the sum borrowed (P) = $5650 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 6780, then the Principal = 100/120 × 6780
= 100 × 6780/120
= 678000/120
= 5650
Thus, Principal = $5650
Thus, the sum borrowed = $5650 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?
(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.
(6) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(7) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
(9) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(10) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.