Simple Interest
Math MCQs

Question :    Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.

Correct Answer  $6820

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (SI) = 3%

Time (t) = 8 years

Thus, Amount (A) = ?

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

Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $5500 × 3% × 8

= $5500 ׳/₁₀₀ × 8

= ^{5500 × 3 × 8}/₁₀₀

= ^{16500 × 8}/₁₀₀

= ¹³²⁰⁰⁰/₁₀₀

= $1320

Thus, Simple Interest = $1320

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 = $5500 + $1320

= $6820

Thus, Amount to be paid = $6820 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 = $5500

Rate of Simple Interest (SI) or (R) = 3%

And, Time (t) = 8 years

Thus, Amount (A)

= $5500 + ($5500 × 3% × 8)

= $5500 + ($5500 ׳/₁₀₀ × 8)

= $5500 + (^{5500 × 3 × 8}/₁₀₀)

= $5500 + (^{16500 × 8}/₁₀₀)

= $5500 + (¹³²⁰⁰⁰/₁₀₀)

= $5500 + $1320 = $6820

Thus, Amount (A) to be paid = $6820 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 3%

This, means, $3 per $100 per year

∵ For $100, the simple interest for 1 year = $3

∴ For $1, the simple interest for 1 year = ³/₁₀₀

∴ For $5500, the simple interest in 1 year

= ³/₁₀₀ × 5500

= ^{3 × 5500}/₁₀₀

= ¹⁶⁵⁰⁰/₁₀₀ = $165

Thus, simple interest for 1 year = $165

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $165 × 8 = $1320

Thus, Simple Interest (SI) = $1320

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $1320

= $6820

Thus, Amount to be paid = $6820 Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?

(4) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?

(6) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.

(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?

(8) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.

(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?