Simple Interest
Math MCQs

Question :    If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $5162

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

$5162 = P (1 + 4% × 4)

⇒ $5162 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5162 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5162 = P (1 + ¹⁶/₁₀₀)

⇒ $5162 = P (^{100 + 16}/₁₀₀)

⇒ $5162 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5162

⇒ P = ⁵¹⁶²/_¹¹⁶/100

⇒ P = 5162 × ¹⁰⁰/₁₁₆

⇒ P = ^{5162 × 100}/₁₁₆

⇒ P = ⁵¹⁶²⁰⁰/₁₁₆

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 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 5162, then the Principal = ¹⁰⁰/₁₁₆ × 5162

= ^{100 × 5162}/₁₁₆

= ⁵¹⁶²⁰⁰/₁₁₆

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

(2) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(3) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?

(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.

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

(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

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

(8) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.