Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

Correct Answer  $10588.5

Solution & Explanation

Solution

Given,

Principal (P) = $5850

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) = $5850 × 9% × 9

= $5850 ×⁹/₁₀₀ × 9

= ^{5850 × 9 × 9}/₁₀₀

= ^{52650 × 9}/₁₀₀

= ⁴⁷³⁸⁵⁰/₁₀₀

= $4738.5

Thus, Simple Interest = $4738.5

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 = $5850 + $4738.5

= $10588.5

Thus, Amount to be paid = $10588.5 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 = $5850

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5850 + ($5850 × 9% × 9)

= $5850 + ($5850 ×⁹/₁₀₀ × 9)

= $5850 + (^{5850 × 9 × 9}/₁₀₀)

= $5850 + (^{52650 × 9}/₁₀₀)

= $5850 + (⁴⁷³⁸⁵⁰/₁₀₀)

= $5850 + $4738.5 = $10588.5

Thus, Amount (A) to be paid = $10588.5 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 $5850, the simple interest in 1 year

= ⁹/₁₀₀ × 5850

= ^{9 × 5850}/₁₀₀

= ⁵²⁶⁵⁰/₁₀₀ = $526.5

Thus, simple interest for 1 year = $526.5

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $526.5 × 9 = $4738.5

Thus, Simple Interest (SI) = $4738.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5850 + $4738.5

= $10588.5

Thus, Amount to be paid = $10588.5 Answer

Similar Questions

(1) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?

(2) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.

(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.

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

(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.

(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?

(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?