Simple Interest
Math MCQs

Question :    If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $3888

Rate of Simple Interest (R) = 2%

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

$3888 = P (1 + 2% × 4)

⇒ $3888 = P (1 + ²/₁₀₀ × 4)

⇒ $3888 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3888 = P (1 + ⁸/₁₀₀)

⇒ $3888 = P (^{100 + 8}/₁₀₀)

⇒ $3888 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3888

⇒ P = ³⁸⁸⁸/_¹⁰⁸/100

⇒ P = 3888 × ¹⁰⁰/₁₀₈

⇒ P = ^{3888 × 100}/₁₀₈

⇒ P = ³⁸⁸⁸⁰⁰/₁₀₈

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 3888, then the Principal = ¹⁰⁰/₁₀₈ × 3888

= ^{100 × 3888}/₁₀₈

= ³⁸⁸⁸⁰⁰/₁₀₈

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 4 years.

(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(4) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?

(5) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?

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

(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.