Simple Interest
Math MCQs

Question :    What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?

Correct Answer  $5390

Solution & Explanation

Solution

Given,

Principal (P) = $3500

Rate of Simple Interest (SI) = 9%

Time (t) = 6 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% per annum.

Method (1) Using Formula

Calculation of Simple Interest

Formula to Calculate Simple Interest

Simple Interest (SI) = Principal × Rate × Time

Thus, Simple Interest (SI) = $3500 × 9% × 6

= $3500 ×⁹/₁₀₀ × 6

= ^{3500 × 9 × 6}/₁₀₀

= ^{31500 × 6}/₁₀₀

= ¹⁸⁹⁰⁰⁰/₁₀₀

= $1890

Thus, Simple Interest = $1890

Calculation of Amount

The total money paid to the lender by a borrower is called the Amount.

In other words, sum of priciple and interest is called the Amount.

Formula to Calculate the Amount

Amount = Principal + Interest

Thus, Amount = $3500 + $1890

= $5390

Thus, Amount to be paid = $5390 Answer

Method (2)

Calculation of Amount when Principal, Rate of Simple Interest and Time are given

Calculation of Amount directly using Principal, SI, and Time

Formula to calculate the Amount

Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)

⇒ A = P + PRT

Here in the question, P = $3500

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 6 years

Thus, Amount (A)

= $3500 + ($3500 × 9% × 6)

= $3500 + ($3500 ×⁹/₁₀₀ × 6)

= $3500 + (^{3500 × 9 × 6}/₁₀₀)

= $3500 + (^{31500 × 6}/₁₀₀)

= $3500 + (¹⁸⁹⁰⁰⁰/₁₀₀)

= $3500 + $1890 = $5390

Thus, Amount (A) to be paid = $5390 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $3500, the simple interest in 1 year

= ⁹/₁₀₀ × 3500

= ^{9 × 3500}/₁₀₀

= ³¹⁵⁰⁰/₁₀₀ = $315

Thus, simple interest for 1 year = $315

Therefore, simple interest for 6 years

= Simple interest for 1 year × 6

= $315 × 6 = $1890

Thus, Simple Interest (SI) = $1890

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3500 + $1890

= $5390

Thus, Amount to be paid = $5390 Answer

Similar Questions

(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?

(2) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.

(4) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(5) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?

(6) Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.

(8) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?

(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?

(10) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.