Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.

Correct Answer  $8393

Solution & Explanation

Solution

Given,

Principal (P) = $5450

Rate of Simple Interest (SI) = 6%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5450 × 6% × 9

= $5450 ×⁶/₁₀₀ × 9

= ^{5450 × 6 × 9}/₁₀₀

= ^{32700 × 9}/₁₀₀

= ²⁹⁴³⁰⁰/₁₀₀

= $2943

Thus, Simple Interest = $2943

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 = $5450 + $2943

= $8393

Thus, Amount to be paid = $8393 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 = $5450

Rate of Simple Interest (SI) or (R) = 6%

And, Time (t) = 9 years

Thus, Amount (A)

= $5450 + ($5450 × 6% × 9)

= $5450 + ($5450 ×⁶/₁₀₀ × 9)

= $5450 + (^{5450 × 6 × 9}/₁₀₀)

= $5450 + (^{32700 × 9}/₁₀₀)

= $5450 + (²⁹⁴³⁰⁰/₁₀₀)

= $5450 + $2943 = $8393

Thus, Amount (A) to be paid = $8393 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 6%

This, means, $6 per $100 per year

∵ For $100, the simple interest for 1 year = $6

∴ For $1, the simple interest for 1 year = ⁶/₁₀₀

∴ For $5450, the simple interest in 1 year

= ⁶/₁₀₀ × 5450

= ^{6 × 5450}/₁₀₀

= ³²⁷⁰⁰/₁₀₀ = $327

Thus, simple interest for 1 year = $327

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $327 × 9 = $2943

Thus, Simple Interest (SI) = $2943

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5450 + $2943

= $8393

Thus, Amount to be paid = $8393 Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.

(2) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.

(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.

(5) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.

(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(9) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.