Simple Interest
Math MCQs

Question :    Robert had to pay $3472 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  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3472

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

$3472 = P (1 + 4% × 3)

⇒ $3472 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3472 = P (1 + ^{4 × 3}/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 = 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 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) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.

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

(4) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

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

(6) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.

(8) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.

(9) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.