Simple Interest
Math MCQs

Question :    Matthew had to pay $4704 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  $4200

Solution & Explanation

Solution

Given,

Amount (A) = $4704

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

$4704 = P (1 + 4% × 3)

⇒ $4704 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4704 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4704 = P (1 + ¹²/₁₀₀)

⇒ $4704 = P (^{100 + 12}/₁₀₀)

⇒ $4704 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4704

⇒ P = ⁴⁷⁰⁴/_¹¹²/100

⇒ P = 4704 × ¹⁰⁰/₁₁₂

⇒ P = ^{4704 × 100}/₁₁₂

⇒ P = ⁴⁷⁰⁴⁰⁰/₁₁₂

⇒ P = $4200

Thus, the sum borrowed (P) = $4200 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 4704, then the Principal = ¹⁰⁰/₁₁₂ × 4704

= ^{100 × 4704}/₁₁₂

= ⁴⁷⁰⁴⁰⁰/₁₁₂

= 4200

Thus, Principal = $4200

Thus, the sum borrowed = $4200 Answer

Similar Questions

(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.

(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.

(3) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?

(4) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.

(5) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.

(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?

(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?

(10) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.