Simple Interest
Math MCQs

Question :    What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?

Correct Answer  $4697

Solution & Explanation

Solution

Given,

Principal (P) = $3050

Rate of Simple Interest (SI) = 9%

Time (t) = 6 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) = $3050 × 9% × 6

= $3050 ×⁹/₁₀₀ × 6

= ^{3050 × 9 × 6}/₁₀₀

= ^{27450 × 6}/₁₀₀

= ¹⁶⁴⁷⁰⁰/₁₀₀

= $1647

Thus, Simple Interest = $1647

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 = $3050 + $1647

= $4697

Thus, Amount to be paid = $4697 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 = $3050

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

And, Time (t) = 6 years

Thus, Amount (A)

= $3050 + ($3050 × 9% × 6)

= $3050 + ($3050 ×⁹/₁₀₀ × 6)

= $3050 + (^{3050 × 9 × 6}/₁₀₀)

= $3050 + (^{27450 × 6}/₁₀₀)

= $3050 + (¹⁶⁴⁷⁰⁰/₁₀₀)

= $3050 + $1647 = $4697

Thus, Amount (A) to be paid = $4697 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 $3050, the simple interest in 1 year

= ⁹/₁₀₀ × 3050

= ^{9 × 3050}/₁₀₀

= ²⁷⁴⁵⁰/₁₀₀ = $274.5

Thus, simple interest for 1 year = $274.5

Therefore, simple interest for 6 years

= Simple interest for 1 year × 6

= $274.5 × 6 = $1647

Thus, Simple Interest (SI) = $1647

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3050 + $1647

= $4697

Thus, Amount to be paid = $4697 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.

(4) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(5) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(6) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.

(10) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.