Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.

Correct Answer  $8100

Solution & Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (SI) = 5%

Time (t) = 10 years

Thus, Amount (A) = ?

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

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5400 × 5% × 10

= $5400 ×⁵/₁₀₀ × 10

= ^{5400 × 5 × 10}/₁₀₀

= ^{27000 × 10}/₁₀₀

= ²⁷⁰⁰⁰⁰/₁₀₀

= $2700

Thus, Simple Interest = $2700

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 = $5400 + $2700

= $8100

Thus, Amount to be paid = $8100 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 = $5400

Rate of Simple Interest (SI) or (R) = 5%

And, Time (t) = 10 years

Thus, Amount (A)

= $5400 + ($5400 × 5% × 10)

= $5400 + ($5400 ×⁵/₁₀₀ × 10)

= $5400 + (^{5400 × 5 × 10}/₁₀₀)

= $5400 + (^{27000 × 10}/₁₀₀)

= $5400 + (²⁷⁰⁰⁰⁰/₁₀₀)

= $5400 + $2700 = $8100

Thus, Amount (A) to be paid = $8100 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $5400, the simple interest in 1 year

= ⁵/₁₀₀ × 5400

= ^{5 × 5400}/₁₀₀

= ²⁷⁰⁰⁰/₁₀₀ = $270

Thus, simple interest for 1 year = $270

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $270 × 10 = $2700

Thus, Simple Interest (SI) = $2700

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5400 + $2700

= $8100

Thus, Amount to be paid = $8100 Answer

Similar Questions

(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?

(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?

(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.

(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 7 years.

(5) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

(6) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(8) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(9) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(10) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.