Simple Interest
Math MCQs

Question :    Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.

Correct Answer  $8034

Solution & Explanation

Solution

Given,

Principal (P) = $5150

Rate of Simple Interest (SI) = 8%

Time (t) = 7 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) = $5150 × 8% × 7

= $5150 ×⁸/₁₀₀ × 7

= ^{5150 × 8 × 7}/₁₀₀

= ^{41200 × 7}/₁₀₀

= ²⁸⁸⁴⁰⁰/₁₀₀

= $2884

Thus, Simple Interest = $2884

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 = $5150 + $2884

= $8034

Thus, Amount to be paid = $8034 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 = $5150

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

And, Time (t) = 7 years

Thus, Amount (A)

= $5150 + ($5150 × 8% × 7)

= $5150 + ($5150 ×⁸/₁₀₀ × 7)

= $5150 + (^{5150 × 8 × 7}/₁₀₀)

= $5150 + (^{41200 × 7}/₁₀₀)

= $5150 + (²⁸⁸⁴⁰⁰/₁₀₀)

= $5150 + $2884 = $8034

Thus, Amount (A) to be paid = $8034 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 $5150, the simple interest in 1 year

= ⁸/₁₀₀ × 5150

= ^{8 × 5150}/₁₀₀

= ⁴¹²⁰⁰/₁₀₀ = $412

Thus, simple interest for 1 year = $412

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $412 × 7 = $2884

Thus, Simple Interest (SI) = $2884

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5150 + $2884

= $8034

Thus, Amount to be paid = $8034 Answer

Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.

(2) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.

(4) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.

(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

(7) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 3 years.

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.