Simple Interest
Math MCQs

Question :    If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4104

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

$4104 = P (1 + 2% × 4)

⇒ $4104 = P (1 + ²/₁₀₀ × 4)

⇒ $4104 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4104 = P (1 + ⁸/₁₀₀)

⇒ $4104 = P (^{100 + 8}/₁₀₀)

⇒ $4104 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4104

⇒ P = ⁴¹⁰⁴/_¹⁰⁸/100

⇒ P = 4104 × ¹⁰⁰/₁₀₈

⇒ P = ^{4104 × 100}/₁₀₈

⇒ P = ⁴¹⁰⁴⁰⁰/₁₀₈

⇒ 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 = 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 4104, then the Principal = ¹⁰⁰/₁₀₈ × 4104

= ^{100 × 4104}/₁₀₈

= ⁴¹⁰⁴⁰⁰/₁₀₈

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(3) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.

(5) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?

(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?

(8) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

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

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.