Question:
How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Amount (A) = $7020
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
$7020 = P (1 + 4% × 5)
⇒ $7020 = P (1 + 4/100 × 5)
⇒ $7020 = P (1 + 4 × 5/100)
⇒ $7020 = P (1 + 20/100)
⇒ $7020 = P (100 + 20/100)
⇒ $7020 = P × 120/100
⇒ P × 120/100 = $7020
⇒ P = 7020/120/100
⇒ P = 7020 × 100/120
⇒ P = 7020 × 100/120
⇒ P = 702000/120
⇒ P = $5850
Thus, the sum borrowed (P) = $5850 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 7020, then the Principal = 100/120 × 7020
= 100 × 7020/120
= 702000/120
= 5850
Thus, Principal = $5850
Thus, the sum borrowed = $5850 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.
(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(3) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(7) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(8) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.