Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

Correct Answer  $9718

Solution & Explanation

Solution

Given,

Principal (P) = $5650

Rate of Simple Interest (SI) = 8%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9

= $5650 ×⁸/₁₀₀ × 9

= ^{5650 × 8 × 9}/₁₀₀

= ^{45200 × 9}/₁₀₀

= ⁴⁰⁶⁸⁰⁰/₁₀₀

= $4068

Thus, Simple Interest = $4068

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 + $4068

= $9718

Thus, Amount to be paid = $9718 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) = 8%

And, Time (t) = 9 years

Thus, Amount (A)

= $5650 + ($5650 × 8% × 9)

= $5650 + ($5650 ×⁸/₁₀₀ × 9)

= $5650 + (^{5650 × 8 × 9}/₁₀₀)

= $5650 + (^{45200 × 9}/₁₀₀)

= $5650 + (⁴⁰⁶⁸⁰⁰/₁₀₀)

= $5650 + $4068 = $9718

Thus, Amount (A) to be paid = $9718 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 8%

This, means, $8 per $100 per year

∵ For $100, the simple interest for 1 year = $8

∴ For $1, the simple interest for 1 year = ⁸/₁₀₀

∴ For $5650, the simple interest in 1 year

= ⁸/₁₀₀ × 5650

= ^{8 × 5650}/₁₀₀

= ⁴⁵²⁰⁰/₁₀₀ = $452

Thus, simple interest for 1 year = $452

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $452 × 9 = $4068

Thus, Simple Interest (SI) = $4068

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5650 + $4068

= $9718

Thus, Amount to be paid = $9718 Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.

(2) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?

(3) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.

(6) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(8) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?

(9) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.