Simple Interest
Math MCQs

Question :    Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.

Correct Answer  $8195

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (SI) = 7%

Time (t) = 7 years

Thus, Amount (A) = ?

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

Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 7

= $5500 ×⁷/₁₀₀ × 7

= ^{5500 × 7 × 7}/₁₀₀

= ^{38500 × 7}/₁₀₀

= ²⁶⁹⁵⁰⁰/₁₀₀

= $2695

Thus, Simple Interest = $2695

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 + $2695

= $8195

Thus, Amount to be paid = $8195 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) = 7%

And, Time (t) = 7 years

Thus, Amount (A)

= $5500 + ($5500 × 7% × 7)

= $5500 + ($5500 ×⁷/₁₀₀ × 7)

= $5500 + (^{5500 × 7 × 7}/₁₀₀)

= $5500 + (^{38500 × 7}/₁₀₀)

= $5500 + (²⁶⁹⁵⁰⁰/₁₀₀)

= $5500 + $2695 = $8195

Thus, Amount (A) to be paid = $8195 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 7%

This, means, $7 per $100 per year

∵ For $100, the simple interest for 1 year = $7

∴ For $1, the simple interest for 1 year = ⁷/₁₀₀

∴ For $5500, the simple interest in 1 year

= ⁷/₁₀₀ × 5500

= ^{7 × 5500}/₁₀₀

= ³⁸⁵⁰⁰/₁₀₀ = $385

Thus, simple interest for 1 year = $385

Therefore, simple interest for 7 years

= Simple interest for 1 year × 7

= $385 × 7 = $2695

Thus, Simple Interest (SI) = $2695

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5500 + $2695

= $8195

Thus, Amount to be paid = $8195 Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(2) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?

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

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?

(5) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.

(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?

(7) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(8) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?

(10) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.