Simple Interest
MCQs Math


Question:     If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.


Correct Answer  $3100

Solution And Explanation

Solution

Given,

Amount (A) = $3472

Rate of Simple Interest (R) = 3%

Time (T) = 4 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

$3472 = P (1 + 3% × 4)

⇒ $3472 = P (1 + 3/100 × 4)

⇒ $3472 = P (1 + 3 × 4/100)

⇒ $3472 = P (1 + 12/100)

⇒ $3472 = P (100 + 12/100)

⇒ $3472 = P × 112/100

⇒ P × 112/100 = $3472

⇒ P = 3472/112/100

⇒ P = 3472 × 100/112

⇒ P = 3472 × 100/112

⇒ P = 347200/112

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/112

∴ If the Amount is 3472, then the Principal = 100/112 × 3472

= 100 × 3472/112

= 347200/112

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer


Similar Questions

(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?

(2) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

(5) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.

(6) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?

(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(10) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.


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