Simple Interest
Math MCQs

Question :    Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3498

Rate of Simple Interest (R) = 2%

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

$3498 = P (1 + 2% × 3)

⇒ $3498 = P (1 + ²/₁₀₀ × 3)

⇒ $3498 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3498 = P (1 + ⁶/₁₀₀)

⇒ $3498 = P (^{100 + 6}/₁₀₀)

⇒ $3498 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3498

⇒ P = ³⁴⁹⁸/_¹⁰⁶/100

⇒ P = 3498 × ¹⁰⁰/₁₀₆

⇒ P = ^{3498 × 100}/₁₀₆

⇒ P = ³⁴⁹⁸⁰⁰/₁₀₆

⇒ P = $3300

Thus, the sum borrowed (P) = $3300 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3498, then the Principal = ¹⁰⁰/₁₀₆ × 3498

= ^{100 × 3498}/₁₀₆

= ³⁴⁹⁸⁰⁰/₁₀₆

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.

(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?

(6) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.

(8) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?

(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.

(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.