Simple Interest
Math MCQs

Question :    If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5336

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

$5336 = P (1 + 4% × 4)

⇒ $5336 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5336 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5336 = P (1 + ¹⁶/₁₀₀)

⇒ $5336 = P (^{100 + 16}/₁₀₀)

⇒ $5336 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5336

⇒ P = ⁵³³⁶/_¹¹⁶/100

⇒ P = 5336 × ¹⁰⁰/₁₁₆

⇒ P = ^{5336 × 100}/₁₁₆

⇒ P = ⁵³³⁶⁰⁰/₁₁₆

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 5336, then the Principal = ¹⁰⁰/₁₁₆ × 5336

= ^{100 × 5336}/₁₁₆

= ⁵³³⁶⁰⁰/₁₁₆

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?

(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.

(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?

(4) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?

(5) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.

(7) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(9) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.