Simple Interest
Math MCQs

Question :    Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.

Correct Answer  $8200

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (SI) = 8%

Time (t) = 8 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) = $5000 × 8% × 8

= $5000 ×⁸/₁₀₀ × 8

= ^{5000 × 8 × 8}/₁₀₀

= ^{40000 × 8}/₁₀₀

= ³²⁰⁰⁰⁰/₁₀₀

= $3200

Thus, Simple Interest = $3200

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 = $5000 + $3200

= $8200

Thus, Amount to be paid = $8200 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 = $5000

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

And, Time (t) = 8 years

Thus, Amount (A)

= $5000 + ($5000 × 8% × 8)

= $5000 + ($5000 ×⁸/₁₀₀ × 8)

= $5000 + (^{5000 × 8 × 8}/₁₀₀)

= $5000 + (^{40000 × 8}/₁₀₀)

= $5000 + (³²⁰⁰⁰⁰/₁₀₀)

= $5000 + $3200 = $8200

Thus, Amount (A) to be paid = $8200 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 $5000, the simple interest in 1 year

= ⁸/₁₀₀ × 5000

= ^{8 × 5000}/₁₀₀

= ⁴⁰⁰⁰⁰/₁₀₀ = $400

Thus, simple interest for 1 year = $400

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $400 × 8 = $3200

Thus, Simple Interest (SI) = $3200

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5000 + $3200

= $8200

Thus, Amount to be paid = $8200 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

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

(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(4) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?

(5) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.

(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?

(8) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(9) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?