Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.

Correct Answer  $10226.5

Solution & Explanation

Solution

Given,

Principal (P) = $5650

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) = $5650 × 9% × 9

= $5650 ×⁹/₁₀₀ × 9

= ^{5650 × 9 × 9}/₁₀₀

= ^{50850 × 9}/₁₀₀

= ⁴⁵⁷⁶⁵⁰/₁₀₀

= $4576.5

Thus, Simple Interest = $4576.5

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 = $5650 + $4576.5

= $10226.5

Thus, Amount to be paid = $10226.5 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 = $5650

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

And, Time (t) = 9 years

Thus, Amount (A)

= $5650 + ($5650 × 9% × 9)

= $5650 + ($5650 ×⁹/₁₀₀ × 9)

= $5650 + (^{5650 × 9 × 9}/₁₀₀)

= $5650 + (^{50850 × 9}/₁₀₀)

= $5650 + (⁴⁵⁷⁶⁵⁰/₁₀₀)

= $5650 + $4576.5 = $10226.5

Thus, Amount (A) to be paid = $10226.5 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 $5650, the simple interest in 1 year

= ⁹/₁₀₀ × 5650

= ^{9 × 5650}/₁₀₀

= ⁵⁰⁸⁵⁰/₁₀₀ = $508.5

Thus, simple interest for 1 year = $508.5

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $508.5 × 9 = $4576.5

Thus, Simple Interest (SI) = $4576.5

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5650 + $4576.5

= $10226.5

Thus, Amount to be paid = $10226.5 Answer

Similar Questions

(1) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?

(2) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.

(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.

(6) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?

(8) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?

(9) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(10) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.