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) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.

(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.

(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?

(5) 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?

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.

(7) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.

(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?

(10) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.