Simple Interest
Math MCQs

Question :    Patricia had to pay $3528 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  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3528

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

$3528 = P (1 + 4% × 3)

⇒ $3528 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3528 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3528 = P (1 + ¹²/₁₀₀)

⇒ $3528 = P (^{100 + 12}/₁₀₀)

⇒ $3528 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3528

⇒ P = ³⁵²⁸/_¹¹²/100

⇒ P = 3528 × ¹⁰⁰/₁₁₂

⇒ P = ^{3528 × 100}/₁₁₂

⇒ P = ³⁵²⁸⁰⁰/₁₁₂

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 3528, then the Principal = ¹⁰⁰/₁₁₂ × 3528

= ^{100 × 3528}/₁₁₂

= ³⁵²⁸⁰⁰/₁₁₂

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.

(2) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.

(5) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.

(6) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?

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

(8) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

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