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) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.

(3) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?

(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(5) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.

(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.

(8) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?

(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(10) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.