Simple Interest
Math MCQs

Question :    If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4816

Rate of Simple Interest (R) = 3%

Time (T) = 4 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 + 3% × 4)

⇒ $4816 = P (1 + ³/₁₀₀ × 4)

⇒ $4816 = P (1 + ^{3 × 4}/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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 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) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.

(2) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?

(4) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?

(5) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?

(7) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

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

(9) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.