Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.

Correct Answer  $9460

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (SI) = 8%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5500 × 8% × 9

= $5500 ×⁸/₁₀₀ × 9

= ^{5500 × 8 × 9}/₁₀₀

= ^{44000 × 9}/₁₀₀

= ³⁹⁶⁰⁰⁰/₁₀₀

= $3960

Thus, Simple Interest = $3960

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 = $5500 + $3960

= $9460

Thus, Amount to be paid = $9460 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 = $5500

Rate of Simple Interest (SI) or (R) = 8%

And, Time (t) = 9 years

Thus, Amount (A)

= $5500 + ($5500 × 8% × 9)

= $5500 + ($5500 ×⁸/₁₀₀ × 9)

= $5500 + (^{5500 × 8 × 9}/₁₀₀)

= $5500 + (^{44000 × 9}/₁₀₀)

= $5500 + (³⁹⁶⁰⁰⁰/₁₀₀)

= $5500 + $3960 = $9460

Thus, Amount (A) to be paid = $9460 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 8%

This, means, $8 per $100 per year

∵ For $100, the simple interest for 1 year = $8

∴ For $1, the simple interest for 1 year = ⁸/₁₀₀

∴ For $5500, the simple interest in 1 year

= ⁸/₁₀₀ × 5500

= ^{8 × 5500}/₁₀₀

= ⁴⁴⁰⁰⁰/₁₀₀ = $440

Thus, simple interest for 1 year = $440

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $440 × 9 = $3960

Thus, Simple Interest (SI) = $3960

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $3960

= $9460

Thus, Amount to be paid = $9460 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(2) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(3) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.

(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.

(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(7) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?

(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.