Simple Interest
Math MCQs

Question :    Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.

Correct Answer  $8400

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (SI) = 5%

Time (t) = 8 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) = $6000 × 5% × 8

= $6000 ×⁵/₁₀₀ × 8

= ^{6000 × 5 × 8}/₁₀₀

= ^{30000 × 8}/₁₀₀

= ²⁴⁰⁰⁰⁰/₁₀₀

= $2400

Thus, Simple Interest = $2400

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 = $6000 + $2400

= $8400

Thus, Amount to be paid = $8400 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 = $6000

Rate of Simple Interest (SI) or (R) = 5%

And, Time (t) = 8 years

Thus, Amount (A)

= $6000 + ($6000 × 5% × 8)

= $6000 + ($6000 ×⁵/₁₀₀ × 8)

= $6000 + (^{6000 × 5 × 8}/₁₀₀)

= $6000 + (^{30000 × 8}/₁₀₀)

= $6000 + (²⁴⁰⁰⁰⁰/₁₀₀)

= $6000 + $2400 = $8400

Thus, Amount (A) to be paid = $8400 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 $6000, the simple interest in 1 year

= ⁵/₁₀₀ × 6000

= ^{5 × 6000}/₁₀₀

= ³⁰⁰⁰⁰/₁₀₀ = $300

Thus, simple interest for 1 year = $300

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $300 × 8 = $2400

Thus, Simple Interest (SI) = $2400

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $6000 + $2400

= $8400

Thus, Amount to be paid = $8400 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(2) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.

(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.

(6) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(7) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.

(9) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.