Simple Interest
Math MCQs

Question :    If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4200

Solution & Explanation

Solution

Given,

Amount (A) = $4704

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

$4704 = P (1 + 3% × 4)

⇒ $4704 = P (1 + ³/₁₀₀ × 4)

⇒ $4704 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4704 = P (1 + ¹²/₁₀₀)

⇒ $4704 = P (^{100 + 12}/₁₀₀)

⇒ $4704 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4704

⇒ P = ⁴⁷⁰⁴/_¹¹²/100

⇒ P = 4704 × ¹⁰⁰/₁₁₂

⇒ P = ^{4704 × 100}/₁₁₂

⇒ P = ⁴⁷⁰⁴⁰⁰/₁₁₂

⇒ P = $4200

Thus, the sum borrowed (P) = $4200 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 4704, then the Principal = ¹⁰⁰/₁₁₂ × 4704

= ^{100 × 4704}/₁₁₂

= ⁴⁷⁰⁴⁰⁰/₁₁₂

= 4200

Thus, Principal = $4200

Thus, the sum borrowed = $4200 Answer

Similar Questions

(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?

(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(3) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.

(4) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 7% simple interest?

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

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.

(8) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?

(9) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.