Simple Interest
MCQs Math


Question:     How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?


Correct Answer  $5300

Solution And Explanation

Solution

Given,

Amount (A) = $5830

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

$5830 = P (1 + 2% × 5)

⇒ $5830 = P (1 + 2/100 × 5)

⇒ $5830 = P (1 + 2 × 5/100)

⇒ $5830 = P (1 + 10/100)

⇒ $5830 = P (100 + 10/100)

⇒ $5830 = P × 110/100

⇒ P × 110/100 = $5830

⇒ P = 5830/110/100

⇒ P = 5830 × 100/110

⇒ P = 5830 × 100/110

⇒ P = 583000/110

⇒ P = $5300

Thus, the sum borrowed (P) = $5300 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 5830, then the Principal = 100/110 × 5830

= 100 × 5830/110

= 583000/110

= 5300

Thus, Principal = $5300

Thus, the sum borrowed = $5300 Answer


Similar Questions

(1) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(5) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.

(8) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.


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