Simple Interest
Math MCQs

Question :    If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3360

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

$3360 = P (1 + 3% × 4)

⇒ $3360 = P (1 + ³/₁₀₀ × 4)

⇒ $3360 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3360 = P (1 + ¹²/₁₀₀)

⇒ $3360 = P (^{100 + 12}/₁₀₀)

⇒ $3360 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3360

⇒ P = ³³⁶⁰/_¹¹²/100

⇒ P = 3360 × ¹⁰⁰/₁₁₂

⇒ P = ^{3360 × 100}/₁₁₂

⇒ P = ³³⁶⁰⁰⁰/₁₁₂

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3360, then the Principal = ¹⁰⁰/₁₁₂ × 3360

= ^{100 × 3360}/₁₁₂

= ³³⁶⁰⁰⁰/₁₁₂

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?

(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(3) 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.

(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.

(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

(7) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

(8) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

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

(10) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.