Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

Correct Answer  $8160

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (SI) = 4%

Time (t) = 9 years

Thus, Amount (A) = ?

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

Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $6000 × 4% × 9

= $6000 ×⁴/₁₀₀ × 9

= ^{6000 × 4 × 9}/₁₀₀

= ^{24000 × 9}/₁₀₀

= ²¹⁶⁰⁰⁰/₁₀₀

= $2160

Thus, Simple Interest = $2160

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 = $6000 + $2160

= $8160

Thus, Amount to be paid = $8160 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 = $6000

Rate of Simple Interest (SI) or (R) = 4%

And, Time (t) = 9 years

Thus, Amount (A)

= $6000 + ($6000 × 4% × 9)

= $6000 + ($6000 ×⁴/₁₀₀ × 9)

= $6000 + (^{6000 × 4 × 9}/₁₀₀)

= $6000 + (^{24000 × 9}/₁₀₀)

= $6000 + (²¹⁶⁰⁰⁰/₁₀₀)

= $6000 + $2160 = $8160

Thus, Amount (A) to be paid = $8160 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 4%

This, means, $4 per $100 per year

∵ For $100, the simple interest for 1 year = $4

∴ For $1, the simple interest for 1 year = ⁴/₁₀₀

∴ For $6000, the simple interest in 1 year

= ⁴/₁₀₀ × 6000

= ^{4 × 6000}/₁₀₀

= ²⁴⁰⁰⁰/₁₀₀ = $240

Thus, simple interest for 1 year = $240

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $240 × 9 = $2160

Thus, Simple Interest (SI) = $2160

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $6000 + $2160

= $8160

Thus, Amount to be paid = $8160 Answer

Similar Questions

(1) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.

(5) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(7) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.

(10) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.