Simple Interest
Math MCQs

Question :    Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.

Correct Answer  $8282

Solution & Explanation

Solution

Given,

Principal (P) = $5050

Rate of Simple Interest (SI) = 8%

Time (t) = 8 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) = $5050 × 8% × 8

= $5050 ×⁸/₁₀₀ × 8

= ^{5050 × 8 × 8}/₁₀₀

= ^{40400 × 8}/₁₀₀

= ³²³²⁰⁰/₁₀₀

= $3232

Thus, Simple Interest = $3232

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 = $5050 + $3232

= $8282

Thus, Amount to be paid = $8282 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 = $5050

Rate of Simple Interest (SI) or (R) = 8%

And, Time (t) = 8 years

Thus, Amount (A)

= $5050 + ($5050 × 8% × 8)

= $5050 + ($5050 ×⁸/₁₀₀ × 8)

= $5050 + (^{5050 × 8 × 8}/₁₀₀)

= $5050 + (^{40400 × 8}/₁₀₀)

= $5050 + (³²³²⁰⁰/₁₀₀)

= $5050 + $3232 = $8282

Thus, Amount (A) to be paid = $8282 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 $5050, the simple interest in 1 year

= ⁸/₁₀₀ × 5050

= ^{8 × 5050}/₁₀₀

= ⁴⁰⁴⁰⁰/₁₀₀ = $404

Thus, simple interest for 1 year = $404

Therefore, simple interest for 8 years

= Simple interest for 1 year × 8

= $404 × 8 = $3232

Thus, Simple Interest (SI) = $3232

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5050 + $3232

= $8282

Thus, Amount to be paid = $8282 Answer

Similar Questions

(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.

(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.

(3) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?

(4) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.

(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.

(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?

(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.