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) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.

(3) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(5) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(6) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?

(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?

(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?

(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?