Simple Interest
Math MCQs

Question :    If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4256

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

$4256 = P (1 + 3% × 4)

⇒ $4256 = P (1 + ³/₁₀₀ × 4)

⇒ $4256 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4256 = P (1 + ¹²/₁₀₀)

⇒ $4256 = P (^{100 + 12}/₁₀₀)

⇒ $4256 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4256

⇒ P = ⁴²⁵⁶/_¹¹²/100

⇒ P = 4256 × ¹⁰⁰/₁₁₂

⇒ P = ^{4256 × 100}/₁₁₂

⇒ P = ⁴²⁵⁶⁰⁰/₁₁₂

⇒ P = $3800

Thus, the sum borrowed (P) = $3800 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 4256, then the Principal = ¹⁰⁰/₁₁₂ × 4256

= ^{100 × 4256}/₁₁₂

= ⁴²⁵⁶⁰⁰/₁₁₂

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?

(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.

(6) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?

(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?

(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.