Simple Interest
Math MCQs

Question :    Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.

Correct Answer  $7700

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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) = $5500 × 5% × 8

= $5500 ×⁵/₁₀₀ × 8

= ^{5500 × 5 × 8}/₁₀₀

= ^{27500 × 8}/₁₀₀

= ²²⁰⁰⁰⁰/₁₀₀

= $2200

Thus, Simple Interest = $2200

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 + $2200

= $7700

Thus, Amount to be paid = $7700 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) = 5%

And, Time (t) = 8 years

Thus, Amount (A)

= $5500 + ($5500 × 5% × 8)

= $5500 + ($5500 ×⁵/₁₀₀ × 8)

= $5500 + (^{5500 × 5 × 8}/₁₀₀)

= $5500 + (^{27500 × 8}/₁₀₀)

= $5500 + (²²⁰⁰⁰⁰/₁₀₀)

= $5500 + $2200 = $7700

Thus, Amount (A) to be paid = $7700 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 $5500, the simple interest in 1 year

= ⁵/₁₀₀ × 5500

= ^{5 × 5500}/₁₀₀

= ²⁷⁵⁰⁰/₁₀₀ = $275

Thus, simple interest for 1 year = $275

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $275 × 8 = $2200

Thus, Simple Interest (SI) = $2200

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $2200

= $7700

Thus, Amount to be paid = $7700 Answer

Similar Questions

(1) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 10% simple interest?

(2) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.

(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(9) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?

(10) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.