Simple Interest
Math MCQs

Question :    If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4408

Rate of Simple Interest (R) = 4%

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

$4408 = P (1 + 4% × 4)

⇒ $4408 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4408 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4408 = P (1 + ¹⁶/₁₀₀)

⇒ $4408 = P (^{100 + 16}/₁₀₀)

⇒ $4408 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4408

⇒ P = ⁴⁴⁰⁸/_¹¹⁶/100

⇒ P = 4408 × ¹⁰⁰/₁₁₆

⇒ P = ^{4408 × 100}/₁₁₆

⇒ P = ⁴⁴⁰⁸⁰⁰/₁₁₆

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4408, then the Principal = ¹⁰⁰/₁₁₆ × 4408

= ^{100 × 4408}/₁₁₆

= ⁴⁴⁰⁸⁰⁰/₁₁₆

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?

(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?

(3) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?

(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.

(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.

(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?