Simple Interest
Math MCQs

Question :    Donald had to pay $5040 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  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $5040

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

$5040 = P (1 + 4% × 3)

⇒ $5040 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5040 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5040 = P (1 + ¹²/₁₀₀)

⇒ $5040 = P (^{100 + 12}/₁₀₀)

⇒ $5040 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5040

⇒ P = ⁵⁰⁴⁰/_¹¹²/100

⇒ P = 5040 × ¹⁰⁰/₁₁₂

⇒ P = ^{5040 × 100}/₁₁₂

⇒ P = ⁵⁰⁴⁰⁰⁰/₁₁₂

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 5040, then the Principal = ¹⁰⁰/₁₁₂ × 5040

= ^{100 × 5040}/₁₁₂

= ⁵⁰⁴⁰⁰⁰/₁₁₂

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?

(4) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.

(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?

(8) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.