Question:
How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
Correct Answer
$7600
Solution And Explanation
Solution
Given,
Amount (A) = $9120
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
$9120 = P (1 + 4% × 5)
⇒ $9120 = P (1 + 4/100 × 5)
⇒ $9120 = P (1 + 4 × 5/100)
⇒ $9120 = P (1 + 20/100)
⇒ $9120 = P (100 + 20/100)
⇒ $9120 = P × 120/100
⇒ P × 120/100 = $9120
⇒ P = 9120/120/100
⇒ P = 9120 × 100/120
⇒ P = 9120 × 100/120
⇒ P = 912000/120
⇒ P = $7600
Thus, the sum borrowed (P) = $7600 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 9120, then the Principal = 100/120 × 9120
= 100 × 9120/120
= 912000/120
= 7600
Thus, Principal = $7600
Thus, the sum borrowed = $7600 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.
(2) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?
(3) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(5) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.
(7) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?