Simple Interest
Math MCQs

Question :    If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4988

Rate of Simple Interest (R) = 4%

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

$4988 = P (1 + 4% × 4)

⇒ $4988 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4988 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4988 = P (1 + ¹⁶/₁₀₀)

⇒ $4988 = P (^{100 + 16}/₁₀₀)

⇒ $4988 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4988

⇒ P = ⁴⁹⁸⁸/_¹¹⁶/100

⇒ P = 4988 × ¹⁰⁰/₁₁₆

⇒ P = ^{4988 × 100}/₁₁₆

⇒ P = ⁴⁹⁸⁸⁰⁰/₁₁₆

⇒ 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 = 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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4988, then the Principal = ¹⁰⁰/₁₁₆ × 4988

= ^{100 × 4988}/₁₁₆

= ⁴⁹⁸⁸⁰⁰/₁₁₆

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(2) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

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

(4) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.

(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?

(8) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?

(9) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.