Question:
How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?
Correct Answer
$7350
Solution And Explanation
Solution
Given,
Amount (A) = $8085
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
$8085 = P (1 + 2% × 5)
⇒ $8085 = P (1 + 2/100 × 5)
⇒ $8085 = P (1 + 2 × 5/100)
⇒ $8085 = P (1 + 10/100)
⇒ $8085 = P (100 + 10/100)
⇒ $8085 = P × 110/100
⇒ P × 110/100 = $8085
⇒ P = 8085/110/100
⇒ P = 8085 × 100/110
⇒ P = 8085 × 100/110
⇒ P = 808500/110
⇒ P = $7350
Thus, the sum borrowed (P) = $7350 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 8085, then the Principal = 100/110 × 8085
= 100 × 8085/110
= 808500/110
= 7350
Thus, Principal = $7350
Thus, the sum borrowed = $7350 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.
(3) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?
(5) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?
(8) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(10) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.