Simple Interest
Math MCQs

Question :    Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

Correct Answer  $9180

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (SI) = 8%

Time (t) = 10 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) = $5100 × 8% × 10

= $5100 ×⁸/₁₀₀ × 10

= ^{5100 × 8 × 10}/₁₀₀

= ^{40800 × 10}/₁₀₀

= ⁴⁰⁸⁰⁰⁰/₁₀₀

= $4080

Thus, Simple Interest = $4080

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 = $5100 + $4080

= $9180

Thus, Amount to be paid = $9180 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 = $5100

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

And, Time (t) = 10 years

Thus, Amount (A)

= $5100 + ($5100 × 8% × 10)

= $5100 + ($5100 ×⁸/₁₀₀ × 10)

= $5100 + (^{5100 × 8 × 10}/₁₀₀)

= $5100 + (^{40800 × 10}/₁₀₀)

= $5100 + (⁴⁰⁸⁰⁰⁰/₁₀₀)

= $5100 + $4080 = $9180

Thus, Amount (A) to be paid = $9180 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 $5100, the simple interest in 1 year

= ⁸/₁₀₀ × 5100

= ^{8 × 5100}/₁₀₀

= ⁴⁰⁸⁰⁰/₁₀₀ = $408

Thus, simple interest for 1 year = $408

Therefore, simple interest for 10 years

= Simple interest for 1 year × 10

= $408 × 10 = $4080

Thus, Simple Interest (SI) = $4080

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5100 + $4080

= $9180

Thus, Amount to be paid = $9180 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.

(3) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.

(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.

(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.

(8) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?

(9) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?