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) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.

(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.

(6) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?

(8) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.

(9) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?