Simple Interest
Math MCQs

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 & 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) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(2) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 9% simple interest?

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(6) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?

(7) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?

(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.

(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(10) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.