Simple Interest
Math MCQs

Question :    If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $5104

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

$5104 = P (1 + 4% × 4)

⇒ $5104 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5104 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5104 = P (1 + ¹⁶/₁₀₀)

⇒ $5104 = P (^{100 + 16}/₁₀₀)

⇒ $5104 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5104

⇒ P = ⁵¹⁰⁴/_¹¹⁶/100

⇒ P = 5104 × ¹⁰⁰/₁₁₆

⇒ P = ^{5104 × 100}/₁₁₆

⇒ P = ⁵¹⁰⁴⁰⁰/₁₁₆

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 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 5104, then the Principal = ¹⁰⁰/₁₁₆ × 5104

= ^{100 × 5104}/₁₁₆

= ⁵¹⁰⁴⁰⁰/₁₁₆

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?

(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.

(4) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.

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

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(7) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(8) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.