Simple Interest
MCQs Math


Question:     Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.


Correct Answer  $3300

Solution And Explanation

Solution

Given,

Amount (A) = $3696

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$3696 = P (1 + 4% × 3)

⇒ $3696 = P (1 + 4/100 × 3)

⇒ $3696 = P (1 + 4 × 3/100)

⇒ $3696 = P (1 + 12/100)

⇒ $3696 = P (100 + 12/100)

⇒ $3696 = P × 112/100

⇒ P × 112/100 = $3696

⇒ P = 3696/112/100

⇒ P = 3696 × 100/112

⇒ P = 3696 × 100/112

⇒ P = 369600/112

⇒ P = $3300

Thus, the sum borrowed (P) = $3300 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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 3696, then the Principal = 100/112 × 3696

= 100 × 3696/112

= 369600/112

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer


Similar Questions

(1) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(2) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.

(4) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?

(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.


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