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 David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?

(2) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(3) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.

(4) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(5) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(6) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(7) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

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

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

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.