Simple Interest
Math MCQs

Question :    If Kimberly paid $5208 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4650

Solution & Explanation

Solution

Given,

Amount (A) = $5208

Rate of Simple Interest (R) = 3%

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

$5208 = P (1 + 3% × 4)

⇒ $5208 = P (1 + ³/₁₀₀ × 4)

⇒ $5208 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5208 = P (1 + ¹²/₁₀₀)

⇒ $5208 = P (^{100 + 12}/₁₀₀)

⇒ $5208 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5208

⇒ P = ⁵²⁰⁸/_¹¹²/100

⇒ P = 5208 × ¹⁰⁰/₁₁₂

⇒ P = ^{5208 × 100}/₁₁₂

⇒ P = ⁵²⁰⁸⁰⁰/₁₁₂

⇒ P = $4650

Thus, the sum borrowed (P) = $4650 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 5208, then the Principal = ¹⁰⁰/₁₁₂ × 5208

= ^{100 × 5208}/₁₁₂

= ⁵²⁰⁸⁰⁰/₁₁₂

= 4650

Thus, Principal = $4650

Thus, the sum borrowed = $4650 Answer

Similar Questions

(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.

(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(3) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.

(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

(7) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(9) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?

(10) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.