Simple Interest
Math MCQs

Question :    Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.

Correct Answer  $9204

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (SI) = 7%

Time (t) = 8 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) = $5900 × 7% × 8

= $5900 ×⁷/₁₀₀ × 8

= ^{5900 × 7 × 8}/₁₀₀

= ^{41300 × 8}/₁₀₀

= ³³⁰⁴⁰⁰/₁₀₀

= $3304

Thus, Simple Interest = $3304

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 = $5900 + $3304

= $9204

Thus, Amount to be paid = $9204 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 = $5900

Rate of Simple Interest (SI) or (R) = 7%

And, Time (t) = 8 years

Thus, Amount (A)

= $5900 + ($5900 × 7% × 8)

= $5900 + ($5900 ×⁷/₁₀₀ × 8)

= $5900 + (^{5900 × 7 × 8}/₁₀₀)

= $5900 + (^{41300 × 8}/₁₀₀)

= $5900 + (³³⁰⁴⁰⁰/₁₀₀)

= $5900 + $3304 = $9204

Thus, Amount (A) to be paid = $9204 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 $5900, the simple interest in 1 year

= ⁷/₁₀₀ × 5900

= ^{7 × 5900}/₁₀₀

= ⁴¹³⁰⁰/₁₀₀ = $413

Thus, simple interest for 1 year = $413

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $413 × 8 = $3304

Thus, Simple Interest (SI) = $3304

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5900 + $3304

= $9204

Thus, Amount to be paid = $9204 Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.

(2) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?

(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.

(6) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.

(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.

(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.