Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.

Correct Answer  $10545

Solution & Explanation

Solution

Given,

Principal (P) = $5550

Rate of Simple Interest (SI) = 10%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5550 × 10% × 9

= $5550 ×¹⁰/₁₀₀ × 9

= ^{5550 × 10 × 9}/₁₀₀

= ^{55500 × 9}/₁₀₀

= ⁴⁹⁹⁵⁰⁰/₁₀₀

= $4995

Thus, Simple Interest = $4995

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 = $5550 + $4995

= $10545

Thus, Amount to be paid = $10545 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 = $5550

Rate of Simple Interest (SI) or (R) = 10%

And, Time (t) = 9 years

Thus, Amount (A)

= $5550 + ($5550 × 10% × 9)

= $5550 + ($5550 ×¹⁰/₁₀₀ × 9)

= $5550 + (^{5550 × 10 × 9}/₁₀₀)

= $5550 + (^{55500 × 9}/₁₀₀)

= $5550 + (⁴⁹⁹⁵⁰⁰/₁₀₀)

= $5550 + $4995 = $10545

Thus, Amount (A) to be paid = $10545 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 10%

This, means, $10 per $100 per year

∵ For $100, the simple interest for 1 year = $10

∴ For $1, the simple interest for 1 year = ¹⁰/₁₀₀

∴ For $5550, the simple interest in 1 year

= ¹⁰/₁₀₀ × 5550

= ^{10 × 5550}/₁₀₀

= ⁵⁵⁵⁰⁰/₁₀₀ = $555

Thus, simple interest for 1 year = $555

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $555 × 9 = $4995

Thus, Simple Interest (SI) = $4995

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5550 + $4995

= $10545

Thus, Amount to be paid = $10545 Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.

(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(3) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.

(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.

(6) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

(7) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?

(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.