Simple Interest
Math MCQs

Question :    James had to pay $3180 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  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3180

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

$3180 = P (1 + 2% × 3)

⇒ $3180 = P (1 + ²/₁₀₀ × 3)

⇒ $3180 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3180 = P (1 + ⁶/₁₀₀)

⇒ $3180 = P (^{100 + 6}/₁₀₀)

⇒ $3180 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3180

⇒ P = ³¹⁸⁰/_¹⁰⁶/100

⇒ P = 3180 × ¹⁰⁰/₁₀₆

⇒ P = ^{3180 × 100}/₁₀₆

⇒ P = ³¹⁸⁰⁰⁰/₁₀₆

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3180, then the Principal = ¹⁰⁰/₁₀₆ × 3180

= ^{100 × 3180}/₁₀₆

= ³¹⁸⁰⁰⁰/₁₀₆

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.

(3) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.

(5) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?

(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.

(9) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(10) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.