Simple Interest
Math MCQs

Question :    Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4592

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$4592 = P (1 + 4% × 3)

⇒ $4592 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4592 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4592 = P (1 + ¹²/₁₀₀)

⇒ $4592 = P (^{100 + 12}/₁₀₀)

⇒ $4592 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4592

⇒ P = ⁴⁵⁹²/_¹¹²/100

⇒ P = 4592 × ¹⁰⁰/₁₁₂

⇒ P = ^{4592 × 100}/₁₁₂

⇒ P = ⁴⁵⁹²⁰⁰/₁₁₂

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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 4592, then the Principal = ¹⁰⁰/₁₁₂ × 4592

= ^{100 × 4592}/₁₁₂

= ⁴⁵⁹²⁰⁰/₁₁₂

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.

(2) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.

(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(5) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?

(6) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?

(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

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