Question:
How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?
Correct Answer
$5050
Solution And Explanation
Solution
Given,
Amount (A) = $5555
Rate of Simple Interest (R) = 2%
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
$5555 = P (1 + 2% × 5)
⇒ $5555 = P (1 + 2/100 × 5)
⇒ $5555 = P (1 + 2 × 5/100)
⇒ $5555 = P (1 + 10/100)
⇒ $5555 = P (100 + 10/100)
⇒ $5555 = P × 110/100
⇒ P × 110/100 = $5555
⇒ P = 5555/110/100
⇒ P = 5555 × 100/110
⇒ P = 5555 × 100/110
⇒ P = 555500/110
⇒ P = $5050
Thus, the sum borrowed (P) = $5050 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5555, then the Principal = 100/110 × 5555
= 100 × 5555/110
= 555500/110
= 5050
Thus, Principal = $5050
Thus, the sum borrowed = $5050 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.
(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(9) If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?