Simple Interest
Math MCQs

Question :    What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

Correct Answer  $5313

Solution & Explanation

Solution

Given,

Principal (P) = $3450

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) = $3450 × 9% × 6

= $3450 ×⁹/₁₀₀ × 6

= ^{3450 × 9 × 6}/₁₀₀

= ^{31050 × 6}/₁₀₀

= ¹⁸⁶³⁰⁰/₁₀₀

= $1863

Thus, Simple Interest = $1863

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 = $3450 + $1863

= $5313

Thus, Amount to be paid = $5313 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 = $3450

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

And, Time (t) = 6 years

Thus, Amount (A)

= $3450 + ($3450 × 9% × 6)

= $3450 + ($3450 ×⁹/₁₀₀ × 6)

= $3450 + (^{3450 × 9 × 6}/₁₀₀)

= $3450 + (^{31050 × 6}/₁₀₀)

= $3450 + (¹⁸⁶³⁰⁰/₁₀₀)

= $3450 + $1863 = $5313

Thus, Amount (A) to be paid = $5313 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 $3450, the simple interest in 1 year

= ⁹/₁₀₀ × 3450

= ^{9 × 3450}/₁₀₀

= ³¹⁰⁵⁰/₁₀₀ = $310.5

Thus, simple interest for 1 year = $310.5

Therefore, simple interest for 6 years

= Simple interest for 1 year × 6

= $310.5 × 6 = $1863

Thus, Simple Interest (SI) = $1863

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3450 + $1863

= $5313

Thus, Amount to be paid = $5313 Answer

Similar Questions

(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?

(2) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.

(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.

(8) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?

(10) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.