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) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?

(3) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.

(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?

(5) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 4 years.

(8) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.

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

(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.