Simple Interest
Math MCQs

Question :    Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.

Correct Answer  $3654

Solution & Explanation

Solution

Given,

Principal (P) = $3150

Rate of Simple Interest (SI) = 4%

Time (t) = 4 years

Thus, Amount (A) = ?

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

Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $3150 × 4% × 4

= $3150 ×⁴/₁₀₀ × 4

= ^{3150 × 4 × 4}/₁₀₀

= ^{12600 × 4}/₁₀₀

= ⁵⁰⁴⁰⁰/₁₀₀

= $504

Thus, Simple Interest = $504

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 = $3150 + $504

= $3654

Thus, Amount to be paid = $3654 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 = $3150

Rate of Simple Interest (SI) or (R) = 4%

And, Time (t) = 4 years

Thus, Amount (A)

= $3150 + ($3150 × 4% × 4)

= $3150 + ($3150 ×⁴/₁₀₀ × 4)

= $3150 + (^{3150 × 4 × 4}/₁₀₀)

= $3150 + (^{12600 × 4}/₁₀₀)

= $3150 + (⁵⁰⁴⁰⁰/₁₀₀)

= $3150 + $504 = $3654

Thus, Amount (A) to be paid = $3654 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 4%

This, means, $4 per $100 per year

∵ For $100, the simple interest for 1 year = $4

∴ For $1, the simple interest for 1 year = ⁴/₁₀₀

∴ For $3150, the simple interest in 1 year

= ⁴/₁₀₀ × 3150

= ^{4 × 3150}/₁₀₀

= ¹²⁶⁰⁰/₁₀₀ = $126

Thus, simple interest for 1 year = $126

Therefore, simple interest for 4 years

= Simple interest for 1 year × 4

= $126 × 4 = $504

Thus, Simple Interest (SI) = $504

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3150 + $504

= $3654

Thus, Amount to be paid = $3654 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

(2) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?

(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?

(4) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(5) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(7) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(8) 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.

(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.

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