Simple Interest
Math MCQs

Question :    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.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4816

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

$4816 = P (1 + 4% × 3)

⇒ $4816 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4816 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4816 = P (1 + ¹²/₁₀₀)

⇒ $4816 = P (^{100 + 12}/₁₀₀)

⇒ $4816 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4816

⇒ P = ⁴⁸¹⁶/_¹¹²/100

⇒ P = 4816 × ¹⁰⁰/₁₁₂

⇒ P = ^{4816 × 100}/₁₁₂

⇒ P = ⁴⁸¹⁶⁰⁰/₁₁₂

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 4816, then the Principal = ¹⁰⁰/₁₁₂ × 4816

= ^{100 × 4816}/₁₁₂

= ⁴⁸¹⁶⁰⁰/₁₁₂

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 4 years.

(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.

(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?

(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 Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(7) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?

(10) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.