Question:
How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?
Correct Answer
$6850
Solution And Explanation
Solution
Given,
Amount (A) = $7535
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
$7535 = P (1 + 2% × 5)
⇒ $7535 = P (1 + 2/100 × 5)
⇒ $7535 = P (1 + 2 × 5/100)
⇒ $7535 = P (1 + 10/100)
⇒ $7535 = P (100 + 10/100)
⇒ $7535 = P × 110/100
⇒ P × 110/100 = $7535
⇒ P = 7535/110/100
⇒ P = 7535 × 100/110
⇒ P = 7535 × 100/110
⇒ P = 753500/110
⇒ P = $6850
Thus, the sum borrowed (P) = $6850 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 7535, then the Principal = 100/110 × 7535
= 100 × 7535/110
= 753500/110
= 6850
Thus, Principal = $6850
Thus, the sum borrowed = $6850 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(2) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?
(3) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?
(5) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(6) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(8) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.
(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.