Simple Interest
Math MCQs

Question :    If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3538

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

$3538 = P (1 + 4% × 4)

⇒ $3538 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3538 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3538 = P (1 + ¹⁶/₁₀₀)

⇒ $3538 = P (^{100 + 16}/₁₀₀)

⇒ $3538 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3538

⇒ P = ³⁵³⁸/_¹¹⁶/100

⇒ P = 3538 × ¹⁰⁰/₁₁₆

⇒ P = ^{3538 × 100}/₁₁₆

⇒ P = ³⁵³⁸⁰⁰/₁₁₆

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 3538, then the Principal = ¹⁰⁰/₁₁₆ × 3538

= ^{100 × 3538}/₁₁₆

= ³⁵³⁸⁰⁰/₁₁₆

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.

(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.

(4) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(5) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?

(7) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(10) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.