Simple Interest
Math MCQs

Question :    Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.

Correct Answer  $3967.5

Solution & Explanation

Solution

Given,

Principal (P) = $3450

Rate of Simple Interest (SI) = 5%

Time (t) = 3 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) = $3450 × 5% × 3

= $3450 ×⁵/₁₀₀ × 3

= ^{3450 × 5 × 3}/₁₀₀

= ^{17250 × 3}/₁₀₀

= ⁵¹⁷⁵⁰/₁₀₀

= $517.5

Thus, Simple Interest = $517.5

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 + $517.5

= $3967.5

Thus, Amount to be paid = $3967.5 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) = 5%

And, Time (t) = 3 years

Thus, Amount (A)

= $3450 + ($3450 × 5% × 3)

= $3450 + ($3450 ×⁵/₁₀₀ × 3)

= $3450 + (^{3450 × 5 × 3}/₁₀₀)

= $3450 + (^{17250 × 3}/₁₀₀)

= $3450 + (⁵¹⁷⁵⁰/₁₀₀)

= $3450 + $517.5 = $3967.5

Thus, Amount (A) to be paid = $3967.5 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 $3450, the simple interest in 1 year

= ⁵/₁₀₀ × 3450

= ^{5 × 3450}/₁₀₀

= ¹⁷²⁵⁰/₁₀₀ = $172.5

Thus, simple interest for 1 year = $172.5

Therefore, simple interest for 3 years

= Simple interest for 1 year × 3

= $172.5 × 3 = $517.5

Thus, Simple Interest (SI) = $517.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3450 + $517.5

= $3967.5

Thus, Amount to be paid = $3967.5 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.

(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 2% simple interest?

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.

(4) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.

(8) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 to clear the loan, then find the time period of the loan.

(9) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.