Simple Interest
MCQs Math


Question:     How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?


Correct Answer  $5450

Solution And Explanation

Solution

Given,

Amount (A) = $6540

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

$6540 = P (1 + 4% × 5)

⇒ $6540 = P (1 + 4/100 × 5)

⇒ $6540 = P (1 + 4 × 5/100)

⇒ $6540 = P (1 + 20/100)

⇒ $6540 = P (100 + 20/100)

⇒ $6540 = P × 120/100

⇒ P × 120/100 = $6540

⇒ P = 6540/120/100

⇒ P = 6540 × 100/120

⇒ P = 6540 × 100/120

⇒ P = 654000/120

⇒ P = $5450

Thus, the sum borrowed (P) = $5450 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 6540, then the Principal = 100/120 × 6540

= 100 × 6540/120

= 654000/120

= 5450

Thus, Principal = $5450

Thus, the sum borrowed = $5450 Answer


Similar Questions

(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?

(2) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

(4) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?

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

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.

(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.

(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.


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