Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.

Correct Answer  $10407.5

Solution & Explanation

Solution

Given,

Principal (P) = $5750

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) = $5750 × 9% × 9

= $5750 ×⁹/₁₀₀ × 9

= ^{5750 × 9 × 9}/₁₀₀

= ^{51750 × 9}/₁₀₀

= ⁴⁶⁵⁷⁵⁰/₁₀₀

= $4657.5

Thus, Simple Interest = $4657.5

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 = $5750 + $4657.5

= $10407.5

Thus, Amount to be paid = $10407.5 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 = $5750

Rate of Simple Interest (SI) or (R) = 9%

And, Time (t) = 9 years

Thus, Amount (A)

= $5750 + ($5750 × 9% × 9)

= $5750 + ($5750 ×⁹/₁₀₀ × 9)

= $5750 + (^{5750 × 9 × 9}/₁₀₀)

= $5750 + (^{51750 × 9}/₁₀₀)

= $5750 + (⁴⁶⁵⁷⁵⁰/₁₀₀)

= $5750 + $4657.5 = $10407.5

Thus, Amount (A) to be paid = $10407.5 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 $5750, the simple interest in 1 year

= ⁹/₁₀₀ × 5750

= ^{9 × 5750}/₁₀₀

= ⁵¹⁷⁵⁰/₁₀₀ = $517.5

Thus, simple interest for 1 year = $517.5

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $517.5 × 9 = $4657.5

Thus, Simple Interest (SI) = $4657.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5750 + $4657.5

= $10407.5

Thus, Amount to be paid = $10407.5 Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(2) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.

(4) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.

(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?

(9) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.