Simple Interest
Math MCQs

Question :    If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4950

Solution & Explanation

Solution

Given,

Amount (A) = $5742

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

$5742 = P (1 + 4% × 4)

⇒ $5742 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5742 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5742 = P (1 + ¹⁶/₁₀₀)

⇒ $5742 = P (^{100 + 16}/₁₀₀)

⇒ $5742 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5742

⇒ P = ⁵⁷⁴²/_¹¹⁶/100

⇒ P = 5742 × ¹⁰⁰/₁₁₆

⇒ P = ^{5742 × 100}/₁₁₆

⇒ P = ⁵⁷⁴²⁰⁰/₁₁₆

⇒ P = $4950

Thus, the sum borrowed (P) = $4950 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 5742, then the Principal = ¹⁰⁰/₁₁₆ × 5742

= ^{100 × 5742}/₁₁₆

= ⁵⁷⁴²⁰⁰/₁₁₆

= 4950

Thus, Principal = $4950

Thus, the sum borrowed = $4950 Answer

Similar Questions

(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.

(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?

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

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.

(6) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.

(8) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.