Simple Interest
Math MCQs

Question :    If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5152

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

$5152 = P (1 + 3% × 4)

⇒ $5152 = P (1 + ³/₁₀₀ × 4)

⇒ $5152 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5152 = P (1 + ¹²/₁₀₀)

⇒ $5152 = P (^{100 + 12}/₁₀₀)

⇒ $5152 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5152

⇒ P = ⁵¹⁵²/_¹¹²/100

⇒ P = 5152 × ¹⁰⁰/₁₁₂

⇒ P = ^{5152 × 100}/₁₁₂

⇒ P = ⁵¹⁵²⁰⁰/₁₁₂

⇒ 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 = 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 5152, then the Principal = ¹⁰⁰/₁₁₂ × 5152

= ^{100 × 5152}/₁₁₂

= ⁵¹⁵²⁰⁰/₁₁₂

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 8% simple interest?

(4) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

(5) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(7) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(8) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.

(9) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?

(10) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?