Simple Interest
Math MCQs

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

Correct Answer  $10045.5

Solution & Explanation

Solution

Given,

Principal (P) = $5550

Rate of Simple Interest (SI) = 9%

Time (t) = 9 years

Thus, Amount (A) = ?

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

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

= $5550 ×⁹/₁₀₀ × 9

= ^{5550 × 9 × 9}/₁₀₀

= ^{49950 × 9}/₁₀₀

= ⁴⁴⁹⁵⁵⁰/₁₀₀

= $4495.5

Thus, Simple Interest = $4495.5

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 + $4495.5

= $10045.5

Thus, Amount to be paid = $10045.5 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) = 9%

And, Time (t) = 9 years

Thus, Amount (A)

= $5550 + ($5550 × 9% × 9)

= $5550 + ($5550 ×⁹/₁₀₀ × 9)

= $5550 + (^{5550 × 9 × 9}/₁₀₀)

= $5550 + (^{49950 × 9}/₁₀₀)

= $5550 + (⁴⁴⁹⁵⁵⁰/₁₀₀)

= $5550 + $4495.5 = $10045.5

Thus, Amount (A) to be paid = $10045.5 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 9%

This, means, $9 per $100 per year

∵ For $100, the simple interest for 1 year = $9

∴ For $1, the simple interest for 1 year = ⁹/₁₀₀

∴ For $5550, the simple interest in 1 year

= ⁹/₁₀₀ × 5550

= ^{9 × 5550}/₁₀₀

= ⁴⁹⁹⁵⁰/₁₀₀ = $499.5

Thus, simple interest for 1 year = $499.5

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $499.5 × 9 = $4495.5

Thus, Simple Interest (SI) = $4495.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5550 + $4495.5

= $10045.5

Thus, Amount to be paid = $10045.5 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

(3) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?

(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(7) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(8) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?